Статті в журналах: "Stiff source"

1

Altschuler, Eric. "Stiff shirts a source of inspiration." Nature 543, no. 7644 (March 2017): 179. http://dx.doi.org/10.1038/543179e.

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2

Lorin, E., and V. Seignole. "Convection Systems with Stiff Source Terms." Mathematical Models and Methods in Applied Sciences 13, no. 07 (July 2003): 971–1018. http://dx.doi.org/10.1142/s0218202503002799.

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The aim of this paper is the numerical treatment of some convection systems with stiff relaxation source-terms. We will first define the notion of stiffness for such systems and will select some prototypical and physical problems. We will introduce a new numerical method in order to solve accurately this type of systems. Numerical comparisons will be performed on the evoked problems.

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3

Kumar, Chandan, and Mahesh K. Mishra. "A Multifunctional DSTATCOM Operating Under Stiff Source." IEEE Transactions on Industrial Electronics 61, no. 7 (July 2014): 3131–36. http://dx.doi.org/10.1109/tie.2013.2276778.

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4

Xu, Hongmei, and Weike Wang. "A linear hyperbolic system with stiff source terms." Wuhan University Journal of Natural Sciences 12, no. 2 (March 2007): 207–10. http://dx.doi.org/10.1007/s11859-006-0030-4.

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5

Yong, Wen-an. "Boundary conditions for hyperbolic systems with stiff source terms." Indiana University Mathematics Journal 48, no. 1 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1611.

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6

Svärd, Magnus, and Siddhartha Mishra. "Implicit–explicit schemes for flow equations with stiff source terms." Journal of Computational and Applied Mathematics 235, no. 6 (January 2011): 1564–77. http://dx.doi.org/10.1016/j.cam.2010.08.015.

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7

KARLSEN, K. H., N. H. RISEBRO, and J. D. TOWERS. "FRONT TRACKING FOR SCALAR BALANCE EQUATIONS." Journal of Hyperbolic Differential Equations 01, no. 01 (March 2004): 115–48. http://dx.doi.org/10.1142/s0219891604000068.

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We propose and prove convergence of a front tracking method for scalar conservation laws with source term. The method is based on writing the single conservation law as a 2×2 quasilinear system without a source term, and employ the solution of the Riemann problem for this system in the front tracking procedure. In this way the source term is processed in the Riemann solver, and one avoids using operator splitting. Since we want to treat the resonant regime, classical arguments for bounding the total variation of numerical solutions do not apply here. Instead compactness of a sequence of front tracking solutions is achieved using a variant of the singular mapping technique invented by Temple [69]. The front tracking method has no CFL-condition associated with it, and it does not discriminate between stiff and non-stiff source terms. This makes it an attractive approach for stiff problems, as is demonstrated in numerical examples. In addition, the numerical examples show that the front tracking method is able to preserve steady-state solutions (or achieving them in the long time limit) with good accuracy.

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8

Mishra, Mahesh K., Arindam Ghosh, and Avinash Joshi. "Load compensation for systems with non-stiff source using state feedback." Electric Power Systems Research 67, no. 1 (October 2003): 35–44. http://dx.doi.org/10.1016/s0378-7796(03)00083-x.

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9

Miniati, Francesco, and Phillip Colella. "A modified higher order Godunov’s scheme for stiff source conservative hydrodynamics." Journal of Computational Physics 224, no. 2 (June 2007): 519–38. http://dx.doi.org/10.1016/j.jcp.2006.10.008.

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10

Herty, Michael, and Hui Yu. "Feedback boundary control of linear hyperbolic equations with stiff source term." International Journal of Control 91, no. 1 (January 23, 2017): 230–40. http://dx.doi.org/10.1080/00207179.2016.1276635.

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11

Yong, Wen-An. "Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms." Journal of Differential Equations 155, no. 1 (June 1999): 89–132. http://dx.doi.org/10.1006/jdeq.1998.3584.

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12

Kumar, T. Santosh, CH Ravi Kumar, and M. Mani Shankar. "Mitigation of Power Quality Problems Using Novel DSTATCOM Operating Under Stiff Source." International Journal of Engineering Research 6, no. 12 (2017): 505. http://dx.doi.org/10.5958/2319-6890.2017.00075.7.

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13

Abreu, Eduardo, Abel Bustos, and Wanderson Lambert. "A unsplitting finite volume method for models with stiff relaxation source terms." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 1 (March 2016): 5–20. http://dx.doi.org/10.1007/s00574-016-0118-1.

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14

Chalabi, A. "Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms." Mathematics of Computation 68, no. 227 (February 10, 1999): 955–71. http://dx.doi.org/10.1090/s0025-5718-99-01089-3.

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15

Tang, Tao, Zhen-Huan Teng, and Jinghua Wang. "Convergence analysis of relaxation schemes for conservation laws with stiff source terms." Methods and Applications of Analysis 8, no. 4 (2001): 667–80. http://dx.doi.org/10.4310/maa.2001.v8.n4.a15.

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16

Boscheri, Walter, and Raphaël Loubère. "High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms." Communications in Computational Physics 21, no. 1 (December 5, 2016): 271–312. http://dx.doi.org/10.4208/cicp.oa-2015-0024.

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AbstractIn this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms. This scheme is constructed with a single stencil polynomial reconstruction operator, a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources, a nodal solver with relaxation to determine the mesh motion, a path-conservative integration technique for the treatment of non-conservative products and ana posterioristabilization procedure derived from the so-called Multidimensional Optimal Order Detection (MOOD) paradigm. In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff. The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study. Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D. The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

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17

Roy, SR, and JP Singh. "A Bianchi Type V Universe with Stiff Fluid and Electromagnetic Radiation." Australian Journal of Physics 38, no. 5 (1985): 763. http://dx.doi.org/10.1071/ph850763.

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This paper discusses the possibility of a Bianchi type V universe containing stiff matter and a source-free electromagnetic field which is, of necessity, found to be null. Physical and kinematical consequences of the model have also been considered.

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18

Navaz, Homayun K., and Raymond M. Berg. "Numerical treatment of multi-phase flow equations with chemistry and stiff source terms." Aerospace Science and Technology 2, no. 3 (March 1998): 219–29. http://dx.doi.org/10.1016/s1270-9638(98)80055-2.

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19

Chalabi, Abdallah. "On convergence of numerical schemes for hyperbolic conservation laws with stiff source terms." Mathematics of Computation 66, no. 218 (April 1, 1997): 527–46. http://dx.doi.org/10.1090/s0025-5718-97-00817-x.

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20

Leveque, R. J., and H. C. Yee. "A study of numerical methods for hyperbolic conservation laws with stiff source terms." Journal of Computational Physics 86, no. 1 (January 1990): 187–210. http://dx.doi.org/10.1016/0021-9991(90)90097-k.

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21

Horgan, Huw J., Laurine van Haastrecht, Richard B. Alley, Sridhar Anandakrishnan, Lucas H. Beem, Knut Christianson, Atsuhiro Muto, and Matthew R. Siegfried. "Grounding zone subglacial properties from calibrated active-source seismic methods." Cryosphere 15, no. 4 (April 19, 2021): 1863–80. http://dx.doi.org/10.5194/tc-15-1863-2021.

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Abstract. The grounding zone of Whillans Ice Stream, West Antarctica, exhibits an abrupt transition in basal properties from the grounded ice to the ocean cavity over distances of less than 0.5–1 km. Active-source seismic methods reveal the downglacier-most grounded portion of the ice stream is underlain by a relatively stiff substrate (relatively high shear wave velocities of 1100±430 m s−1) compared to the deformable till found elsewhere beneath the ice stream. Changes in basal reflectivity in our study area cannot be explained by the stage of the tide. Several kilometres upstream of the grounding zone, layers of subglacial water are detected, as are regions that appear to be water layers but are less than the thickness resolvable by our technique. The presence of stiff subglacial sediment and thin water layers upstream of the grounding zone supports previous studies that have proposed the dewatering of sediment within the grounding zone and the trapping of subglacial water upstream of the ocean cavity. The setting enables calibration of our methodology using returns from the floating ice shelf. This allows a comparison of different techniques used to estimate the sizes of the seismic sources, a constraint essential for the accurate recovery of subglacial properties. We find a strong correlation (coefficient of determination=0.46) between our calibrated method and a commonly used multiple-bounce method, but our results also highlight the incomplete knowledge of other factors affecting the amplitude of seismic sources and reflections in the cryosphere.

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22

Kalumbi, Martin, Limbikani Matumba, Beatrice Mtimuni, Agnes Mwangwela, and Aggrey P. Gama. "Hydrothermally Treated Soybeans Can Enrich Maize Stiff Porridge (Africa’s Main Staple) without Negating Sensory Acceptability." Foods 8, no. 12 (December 6, 2019): 650. http://dx.doi.org/10.3390/foods8120650.

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Maize-based stiff porridge, a starchy protein-deficient staple food, dominates among the populations in sub-Saharan Africa (SSA). Unfortunately, this is often consumed along with leafy vegetables since the majority of the population in this region lack resources for the purchase of high protein animal source foods, a situation that exacerbates protein-energy malnutrition. Considering this, the current study evaluated the effect of enriching maize-based stiff porridge with flour made from hydrothermally treated soybeans on consumer acceptability. A total of nine experimental flours were prepared from maize and maize-soybean mixtures following a 32 factorial design involving two factors, namely maize flour type (whole maize, non-soaked dehulled maize, and soaked dehulled maize) and soybean flour proportion (0%, 20%, and 30%). A total of 125 adult consumers from a rural setting in Malawi evaluated maize-based stiff porridges made thereof using a 7-point hedonic scale. Subsequently, the participants were asked to guess an ingredient that was added to some of the test samples. The 10% and 20% soybean-enriched maize-based stiff porridges scored 5/7 and above, with some being statistically similar to plain maize-based stiff porridges. No participant recognized that soybeans were incorporated into the maize-based stiff porridges. The study has clearly demonstrated the potential of enriching maize-based stiff porridge with hydrothermally treated soybeans without compromising consumer acceptability. This innovation could significantly contribute towards reducing the burden of energy-protein under-nutrition in SSA.

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23

Zakerzadeh, Hamed. "Asymptotic analysis of the RS-IMEX scheme for the shallow water equations in one space dimension." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 3 (May 2019): 893–924. http://dx.doi.org/10.1051/m2an/2019005.

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We introduce and analyse the so-called Reference Solution IMplicit-EXplicit scheme as a flux-splitting method for singularly-perturbed systems of balance laws. RS-IMEX scheme’s bottom-line is to use the Taylor expansion of the flux function and the source term around a reference solution (typically the asymptotic limit or an equilibrium solution) to decompose the flux and the source into stiff and non-stiff parts so that the resulting IMEX scheme is Asymptotic Preserving (AP) w.r.t. the singular parameter tending to zero. We prove the asymptotic consistency, asymptotic stability, solvability and well-balancing of the scheme for the case of the one-dimensional shallow water equations when the singular parameter is the Froude number. We will also study several test cases to illustrate the quality of the computed solutions and to confirm the analysis.

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24

Tang, Tao. "Convergence Analysis for Operator-Splitting Methods Applied to Conservation Laws with Stiff Source Terms." SIAM Journal on Numerical Analysis 35, no. 5 (October 1998): 1939–68. http://dx.doi.org/10.1137/s0036142996308927.

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25

Kunjumuhammed, L. P., and M. K. Mishra. "A control algorithm for single-phase active power filter under non-stiff voltage source." IEEE Transactions on Power Electronics 21, no. 3 (May 2006): 822–25. http://dx.doi.org/10.1109/tpel.2006.874939.

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26

Martı́nez, Vicente, and Antonio Marquina. "Computation of travelling wave solutions of scalar conservation laws with a stiff source term." Computers & Fluids 32, no. 8 (September 2003): 1161–78. http://dx.doi.org/10.1016/s0045-7930(02)00079-8.

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27

Hebeker, Friedrich K., and Rolf Rannacher. "An Adaptive Finite Element Method for Unsteady Convection-Dominated Flows with Stiff Source Terms." SIAM Journal on Scientific Computing 21, no. 3 (January 1999): 799–818. http://dx.doi.org/10.1137/s1064827597319039.

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28

Jayaraman, Ramesh, and Aruldoss Albert Victoire. "Implementation of Differential Equation of Single-Phase Source-Load System Based Control Algorithm for Three-Phase DSTATCOM under Stiff Source." Electric Power Components and Systems 45, no. 18 (November 8, 2017): 1985–95. http://dx.doi.org/10.1080/15325008.2017.1362606.

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29

Padmanabhan, Sanosh Kunjalukkal, Francesca Lionetto, Rossella Nisi, Mariangela Stoppa, and Antonio Licciulli. "Sustainable Production of Stiff and Crystalline Bacterial Cellulose from Orange Peel Extract." Sustainability 14, no. 4 (February 16, 2022): 2247. http://dx.doi.org/10.3390/su14042247.

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In this work, a potentially economic and environmentally friendly method for the synthesis of bacterial cellulose (BC) by Gluconacetobacter xylinus from a biomass containing orange peel extract was evaluated. Orange peel extract was used as a culture medium without any hydrolysis treatment, thus speeding up the synthesis procedure. The efficacy of orange peel as a carbon source was compared with that of sucrose. The orange peel extract formed thicker cellulose gels than those formed using sucrose. X-ray diffraction (XRD) revealed both a high crystallinity index and crystallite size of BC nanofibers in samples obtained from orange peel (BC_Orange). Field emission scanning electron microscopy (FE-SEM) revealed a highly densely packed nanofibrous structure (50 nm in diameter). BC_Orange presented a two-fold increase in water holding capacity (WHC), and dynamic mechanical analysis (DMA) showed a 44% increase in storage modulus compared to sucrose derived BC. These results showed that the naturally available carbon sources derived from orange peel extract can be effectively used for BC production. The orange-based culture medium can be considered a profitable alternative to the generation of high-value products in a virtuous circular economy model.

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30

Pichard, Teddy, Nina Aguillon, Bruno Després, Edwige Godlewski, and Michael Ndjinga. "Existence and uniqueness of generalized solutions to hyperbolic systems with linear fluxes and stiff sources." Journal of Hyperbolic Differential Equations 18, no. 03 (September 2021): 653–700. http://dx.doi.org/10.1142/s021989162150020x.

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Motivated by the modeling of boiling two-phase flows, we study systems of balance laws with a source term defined as a discontinuous function of the unknown. Due to this discontinuous source term, the classical theory of partial differential equations (PDEs) is not sufficient here. Restricting to a simpler system with linear fluxes, a notion of generalized solution is developed. An important point in the construction of a solution is that the curve along which the source jumps, which we call the boiling curve, must never be tangent to the characteristics. This leads to exhibit sufficient conditions which ensure the existence and uniqueness of a solution in two different situations: first when the initial data is smooth and such that the boiling curve is either overcharacteristic or subcharacteristic; then with discontinuous initial data in the case of Riemann problems. A numerical illustration is given in this last case.

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31

Bolduc, M., B. Terreault, A. Reguer, E. Shaffer, and R. G. St-Jacques. "Optimum tribological improvement of aluminum using oxygen plasma source ion implantation." Journal of Materials Research 18, no. 8 (August 2003): 1761–64. http://dx.doi.org/10.1557/jmr.2003.0244.

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Aluminum and its alloys show poor tribological properties. Oxygen plasma source ion implantation is an emerging technology for the improvement of the surface mechanical properties of these materials. We found an optimum O ion dose, corresponding to 35 at.% O, for which we were able to obtain nanohardness enhancements by factors of 2× and 3× for pure and alloyed (AA7075) Al, respectively. Nanoscratch test results showed reductions in the scratch depths and the friction coefficients by nearly the same factors. It is also important to control the process temperature (∼160 °C). These improvements are due to the formation of a smooth, stiff, but nonbrittle metal–oxide (Al–Al2O3) nanocomposite.

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32

Wang, Wei, Chi-Wang Shu, H. C. Yee, and Björn Sjögreen. "High order finite difference methods with subcell resolution for advection equations with stiff source terms." Journal of Computational Physics 231, no. 1 (January 2012): 190–214. http://dx.doi.org/10.1016/j.jcp.2011.08.031.

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33

Batishchev, Denis, Andrey Kosarev, Ivan Vasyukov, and Andrey Zhivodernikov. "Application of the EDA- software LTspice for Computer Simulation of Transient Modes in Electrical Circuits." Известия высших учебных заведений. Электромеханика 65, no. 3 (2022): 10–19. http://dx.doi.org/10.17213/0136-3360-2022-3-10-19.

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The purpose of this article is to evaluate the reliability of particular solutions obtained in practice for stiff systems of ordinary differential equations using the LTspice software. Testing was carried out in two directions: experimental testing of the software on known practical problems with a known experimental solution and mathematical testing of the software solver on known mathematical problems with a known asymptotic or analytical solution. The results of calculations for test problems of circuit analysis from the set of CircuitSim90 circuits that are difficult to solve and the set of tests for stiff and non-stiff INdAM-Bari ODEs are presented. A comparative assessment of the obtained results with the test ones was made. The effectiveness of using the LTspice software for solving such problems is shown by the example of calculating a high-voltage pulsed power source for electron beam welding with setting the solver parame-ters to obtain reliable and accurate results of numerical simulation.

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34

Reisinger, Christoph, and Yufei Zhang. "Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems." Analysis and Applications 18, no. 06 (July 23, 2020): 951–99. http://dx.doi.org/10.1142/s0219530520500116.

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In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network (DNN), whose complexity grows at most polynomially in both the dimension of the state equation and the reciprocal of the required accuracy. Such nonlinear stiff systems may arise, for example, from Galerkin approximations of controlled stochastic partial differential equations (SPDEs), or controlled PDEs with uncertain initial conditions and source terms. This implies that DNNs can break the curse of dimensionality in numerical approximations and optimal control of PDEs and SPDEs. The main ingredient of our proof is to construct a suitable discrete-time system to effectively approximate the evolution of the underlying stochastic dynamics. Similar ideas can also be applied to obtain expression rates of DNNs for value functions induced by stiff systems with regime switching coefficients and driven by general Lévy noise.

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35

Mulargia, Francesco, Silvia Castellaro, and Gianluca Vinco. "Measuring shear wave velocity, Vs, of a hidden layer: an application to soil improvement under roads." Canadian Geotechnical Journal 52, no. 6 (June 2015): 721–31. http://dx.doi.org/10.1139/cgj-2014-0125.

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In a number of practical cases, a typical one being the investigation of the subsoil properties below roads or foundations, one faces the problem of measuring the elastic properties of a geological layer (here called “hidden layer”) underlying a more compact and rigid surface layer. In such cases, the effectiveness of common surface seismic methods is poor for different reasons, but mostly linked to the reflection–transmission properties of the waves at a stiff-to-soft interface. Borehole methods are more efficient, but expensive and only provide vertical information at certain points. Attempts carried out in the past to characterize the hidden layer properties through surface seismic techniques consisted in placing the seismic source on the surface alongside, but off the stiff artificial layer (road or foundation). An alternative approach is presented based on placing the seismic source just below the stiff artificial layer. In cases where soil improvement–compaction are carried out through injection of expanding resins, then the hidden layer can be easily reached via the injecting tools and in some cases (e.g., urban settings characterized by laterally continuous artificial layers or roads constructed on embankments) this can be the only viable option. The results obtained from this approach using a number of practical cases where roads affected by differential sinking have later been compacted will be presented. The average soil improvement that can be achieved with the specific kind of expanding resin used in this study is then quantified.

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36

Li, Caoyang, David Herrin, John Baker, and Asad M. Sardar. "Simulation of rubber grommets and correlation with test at low frequencies." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 1 (August 1, 2021): 5740–47. http://dx.doi.org/10.3397/in-2021-3246.

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Residential air conditioning units include several sources which can lead to vibrational and noise issues. The most important structure-borne source is the compressor which controls the noise and vibration in certain frequency ranges. Compressors are mounted on four relatively stiff rubber grommets which partially isolate the basepan from the compressor motion while also ensuring that the compressor does not move too much. In this work, the grommets are simulated using the finite element method and results are correlated with measurement results with good agreement. It is demonstrated that the hyperelastic properties of the grommets should be increased due to the Payne effect to improve correlation.

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37

Yu, Bin, Linying Li, Bin Zhang, and Jianhang Wang. "An Approach to Obtain the Correct Shock Speed for Euler Equations with Stiff Detonation." Communications in Computational Physics 22, no. 1 (May 3, 2017): 259–84. http://dx.doi.org/10.4208/cicp.oa-2015-0008.

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AbstractIncorrect propagation speed of discontinuities may occur by straightforward application of standard dissipative schemes for problems that contain stiff source terms for underresolved grids even for time steps within the CFL condition. By examining the dissipative discretized counterpart of the Euler equations for a detonation problem that consists of a single reaction, detailed analysis on the spurious wave pattern is presented employing the fractional step method, which utilizes the Strang splitting. With the help of physical arguments, a threshold values method (TVM), which can be extended to more complicated stiff problems, is developed to eliminate the wrong shock speed phenomena. Several single reaction detonations as well as multispecies and multi-reaction detonation test cases with strong stiffness are examined to illustrate the performance of the TVM approach.

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38

Setare, M. R. "The self-gravitational corrections as the source for stiff matter on the brane in SAdS5 bulk." Physics Letters B 612, no. 3-4 (April 2005): 100–104. http://dx.doi.org/10.1016/j.physletb.2005.03.029.

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39

Roedig, C., O. Zanotti, and D. Alic. "General relativistic radiation hydrodynamics of accretion flows - II. Treating stiff source terms and exploring physical limitations." Monthly Notices of the Royal Astronomical Society 426, no. 2 (October 1, 2012): 1613–31. http://dx.doi.org/10.1111/j.1365-2966.2012.21821.x.

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40

Choudhary, Niraj Kumar, Soumya Ranjan Mohanty, and Ravindra Kumar Singh. "Power Management in Microgrid: Analysis in Grid Connected and Islanded Mode of Operation." International Journal of Applied Power Engineering (IJAPE) 6, no. 3 (December 1, 2017): 160. http://dx.doi.org/10.11591/ijape.v6.i3.pp160-170.

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This paper presents an investigation about the impact of integrating renewable energy based generation sources on the existing distribution system in terms of load sharing. The study of load sharing among various distributed generators (DGs) and utility grid has been performed for two cases: (a) when equivalent source based DG is connected and (b) when real PV/Fuel cell based DG is properly integrated to the distribution system. The real photovoltaic and fuel cell based DG do not behave as stiff current/voltage source due to disturbances happening either internally in system known as parametric uncertainties or due to external disturbances like weather conditions, load change etc. Further it has been observed with extensive analysis using simulation result, that even though all DGs are of equal capacity in their generation but when the load is either increased or decreased this doesn’t essentially guarantee that all DGs will equally share the active and reactive power demand.

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41

Choudhary, Niraj Kumar, Soumya Ranjan Mohanty, and Ravindra Kumar Singh. "Power Management in Microgrid: Analysis in Grid Connected and Islanded Mode of Operation." International Journal of Applied Power Engineering (IJAPE) 6, no. 3 (December 1, 2017): 163. http://dx.doi.org/10.11591/ijape.v6.i3.pp163-173.

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This paper presents an investigation about the impact of integrating renewable energy based generation sources on the existing distribution system in terms of load sharing. The study of load sharing among various distributed generators (DGs) and utility grid has been performed for two cases: (a) when equivalent source based DG is connected and (b) when real PV/Fuel cell based DG is properly integrated to the distribution system. The real photovoltaic and fuel cell based DG do not behave as stiff current/voltage source due to disturbances happening either internally in system known as parametric uncertainties or due to external disturbances like weather conditions, load change etc. Further it has been observed with extensive analysis using simulation result, that even though all DGs are of equal capacity in their generation but when the load is either increased or decreased this doesn’t essentially guarantee that all DGs will equally share the active and reactive power demand

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42

Ji, L., B. R. Mace, and R. J. Pinnington. "Estimation of power transmission to a flexible receiver from a stiff source using a power mode approach." Journal of Sound and Vibration 268, no. 3 (November 2003): 525–42. http://dx.doi.org/10.1016/s0022-460x(03)00255-4.

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43

Abreu, Eduardo, Abel Bustos, and Wanderson Lambert. "Non-monotonic traveling wave and computational solutions for gas dynamics Euler equations with stiff relaxation source terms." Computers & Mathematics with Applications 70, no. 9 (November 2015): 2155–76. http://dx.doi.org/10.1016/j.camwa.2015.07.002.

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44

Mazzia, Francesca, Jeff R. Cash, and Karline Soetaert. "A Test Set for stiff Initial Value Problem Solvers in the open source software R: Package deTestSet." Journal of Computational and Applied Mathematics 236, no. 16 (October 2012): 4119–31. http://dx.doi.org/10.1016/j.cam.2012.03.014.

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45

Huang, Juntao, and Chi-Wang Shu. "Bound-preserving modified exponential Runge–Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms." Journal of Computational Physics 361 (May 2018): 111–35. http://dx.doi.org/10.1016/j.jcp.2018.01.051.

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46

Herdiana, Ratna. "NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD." Journal of Fundamental Mathematics and Applications (JFMA) 3, no. 1 (June 10, 2020): 72–83. http://dx.doi.org/10.14710/jfma.v3i1.7416.

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Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.

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47

SETARE, MOHAMMAD R., and ELIAS C. VAGENAS. "SELF-GRAVITATIONAL CORRECTIONS TO THE CARDY–VERLINDE FORMULA AND THE FRW BRANE COSMOLOGY IN SdS5 BULK." International Journal of Modern Physics A 20, no. 30 (December 10, 2005): 7219–32. http://dx.doi.org/10.1142/s0217751x05023888.

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The semiclassical corrections to the Cardy–Verlinde entropy of a five-dimensional Schwarzschild de-Sitter black hole ( SdS 5) are explicitly evaluated. These corrections are considered within the context of KKW analysis and arise as a result of the self-gravitation effect. In addition, a four-dimensional spacelike brane is considered as the boundary of the SdS 5 bulk background. It is already known that the induced geometry of the brane is exactly given by that of a radiation-dominated FRW universe. By exploiting the CFT/FRW-cosmology relation, we derive the self-gravitational corrections to the first Friedmann-like equation which is the equation of the brane motion. The additional term that arises due to the semiclassical analysis can be viewed as stiff matter where the self-gravitational corrections act as the source for it. This result is contrary to standard analysis that regards the charge of SdS 5 bulk black hole as the source for stiff matter. Furthermore, we rewrite the Friedmann-like equation in such a way that it represents the conservation equation of energy of a point particle moving in a one-dimensional effective potential. The self-gravitational corrections to the effective potential and, consequently, to the point particle's motion are obtained. A short analysis on the asymptotic behavior of the four-dimensional brane is presented.

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48

Yee, H. C., D. V. Kotov, Wei Wang, and Chi-Wang Shu. "Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities." Journal of Computational Physics 241 (May 2013): 266–91. http://dx.doi.org/10.1016/j.jcp.2013.01.028.

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49

Tudor, M. "A test of numerical instability and stiffness in the parametrizations of the ARPÉGE and ALADIN models." Geoscientific Model Development 6, no. 4 (July 5, 2013): 901–13. http://dx.doi.org/10.5194/gmd-6-901-2013.

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Abstract. Meteorological numerical weather prediction (NWP) models solve a system of partial differential equations in time and space. Semi-lagrangian advection schemes allow for long time steps. These longer time steps can result in instabilities occurring in the model physics. A system of differential equations in which some solution components decay more rapidly than others is stiff. In this case it is stability rather than accuracy that restricts the time step. The vertical diffusion parametrization can cause fast non-meteorological oscillations around the slowly evolving true solution (fibrillations). These are treated with an anti-fibrillation scheme, but small oscillations remain in operational weather forecasts using ARPÉGE and ALADIN models. In this paper, a simple test is designed to reveal if the formulation of particular a physical parametrization is a stiff problem or potentially numerically unstable in combination with any other part of the model. When the test is applied to a stable scheme, the solution remains stable. However, applying the test to a potentially unstable scheme yields a solution with fibrillations of substantial amplitude. The parametrizations of the NWP model ARPÉGE were tested one by one to see which one may be the source of unstable model behaviour. The test identified the set of equations in the stratiform precipitation scheme (a diagnostic Kessler-type scheme) as a stiff problem, particularly the combination of terms arising due to the evaporation of snow.

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Frankel, Arthur, David Carver, Edward Cranswick, Mark Meremonte, Thomas Bice, and Dee Overturf. "Site response for Seattle and source parameters of earthquakes in the Puget Sound Region." Bulletin of the Seismological Society of America 89, no. 2 (April 1, 1999): 468–83. http://dx.doi.org/10.1785/bssa0890020468.

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Abstract We analyzed seismograms from 21 earthquakes (ML 2.0-4.9) recorded by digital seismographs we deployed in urban Seattle to determine site response and earthquake stress drops. The seismometers were situated on a wide variety of geologic units, including artificial fill (e.g., Kingdome, Harbor Island), Pleistocene age soils (glacial till and outwash deposits of Seattle's hills), modified land (downtown Seattle, Space Needle), and Tertiary sedimentary rock. Two mainshock-aftershock sequences were recorded: the June 1997 Bremerton sequence (mainshock ML 4.9) and the February 1997 South Seattle sequence (mainshock ML 3.5), along with other events in the Puget Sound region. We developed a new inversion procedure to estimate site response, source corner frequencies, and seismic moments from the S-wave spectra. This inversion uses corner frequencies determined from spectral ratios of mainshock-aftershock pairs as constraints. The site responses found from the inversion are not relative to the rock site but are relative to an idealized site with a flat frequency response. The response of the rock site is also found from the inversion. The inversion results show high response for the sites on artificial fill, more moderate amplification for most sites on stiff Pleistocene soils or modified land, and low response for the rock site. Some sites display resonances, such as a strong 2-Hz resonance at our site near the Kingdome, which is caused by the surficial layers of fill and younger alluvium. The sites in West Seattle exhibit high amplification, even though they are on relatively stiff soils of glacial outwash. This may be partly caused by basin surface waves produced by conversion of incident S waves. This high response in West Seattle is consistent with damage reports from the 1949 (mb 7.1) and 1965 (mb 6.5) earthquakes. Stress-drop estimates for the events we recorded were generally low, between 0.4 and 25 bars, although some of the events may have had higher stress drops that could not be resolved because of the limited passband. We calculated a stress drop of 24 bars for the Bremerton mainshock and 10 bars for the South Seattle mainshock.

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