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Добірка наукової літератури з теми "Integration numerical"

Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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Статті в журналах з теми "Integration numerical"

Matušů, Josef, Gejza Dohnal, and Martin Matušů. "On one method of numerical integration." Applications of Mathematics 36, no. 4 (1991): 241–63. http://dx.doi.org/10.21136/am.1991.104464.

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Faou, Erwan, Ernst Hairer, Marlis Hochbruck, and Christian Lubich. "Geometric Numerical Integration." Oberwolfach Reports 13, no. 1 (2016): 869–948. http://dx.doi.org/10.4171/owr/2016/18.

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Elliott, David, H. Brass, and G. Hammerlin. "Numerical Integration IV." Mathematics of Computation 64, no. 210 (April 1995): 901. http://dx.doi.org/10.2307/2153467.

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G., W., H. Brass, and G. H. Hammerlin. "Numerical Integration III." Mathematics of Computation 53, no. 187 (July 1989): 451. http://dx.doi.org/10.2307/2008381.

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Dyer, Stephen, and Justin Dyer. "bythenumbers - Numerical integration." IEEE Instrumentation & Measurement Magazine 11, no. 2 (April 2008): 47–49. http://dx.doi.org/10.1109/mim.2008.4483733.

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Clegg, D. B., and A. N. Richmond. "Perfect numerical integration." International Journal of Mathematical Education in Science and Technology 18, no. 4 (July 1987): 519–25. http://dx.doi.org/10.1080/0020739870180403.

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Zadiraka, V. K., L. V. Luts, and I. V. Shvidchenko. "Optimal Numerical Integration." Cybernetics and Computer Technologies, no. 4 (December 31, 2020): 47–64. http://dx.doi.org/10.34229/2707-451x.20.4.4.

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Introduction. In many applied problems, such as statistical data processing, digital filtering, computed tomography, pattern recognition, and many others, there is a need for numerical integration, moreover, with a given (often quite high) accuracy. Classical quadrature formulas cannot always provide the required accuracy, since, as a rule, they do not take into account the oscillation of the integrand. In this regard, the development of methods for constructing optimal in accuracy (and close to them) quadrature formulas for the integration of rapidly oscillating functions is rather important and topical problem of computational mathematics. The purpose of the article is to use the example of constructing optimal in accuracy (and close to them) quadrature formulas for calculating integrals for integrands of various degrees of smoothness and for oscillating factors of different types and constructing a priori estimates of their total error, as well as applying to them of the theory of testing the quality of algorithms-programs to create a theory of optimal numerical integration. Results. The optimal in accuracy (and close to them) quadrature formulas for calculating the Fourier transform, wavelet transforms, and Bessel transform were constructed both in the classical formulation of the problem and for interpolation classes of functions corresponding to the case when the information operator about the integrand is given by a fixed table of its values. The paper considers a passive pure minimax strategy for solving the problem. Within the framework of this strategy, we used the method of “caps” by N. S. Bakhvalov and the method of boundary functions developed at the V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine. Great attention is paid to the quality of the error estimates and the methods to obtain them. The article describes some aspects of the theory of algorithms-programs testing and presents the results of testing the constructed quadrature formulas for calculating integrals of rapidly oscillating functions and estimates of their characteristics. The problem of determining the ranges of admissible values of control parameters of programs for calculating integrals with the required accuracy, as well as their best values for integration with the minimum possible error, is considered for programs calculating a priori estimates of characteristics. Conclusions. The results obtained make it possible to create a theory of optimal integration, which makes it possible to reasonably choose and efficiently use computational resources to find the value of the integral with a given accuracy or with the minimum possible error. Keywords: quadrature formula, optimal algorithm, interpolation class, rapidly oscillating function, quality testing.

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Burk, Frank. "Numerical Integration via Integration by Parts." College Mathematics Journal 17, no. 5 (November 1986): 418. http://dx.doi.org/10.2307/2686254.

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Burk, Frank. "Numerical Integration via Integration by Parts." College Mathematics Journal 17, no. 5 (November 1986): 418–22. http://dx.doi.org/10.1080/07468342.1986.11972993.

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Arthur, D. W., Philip J. Davis, and Philip Rabinowitz. "Methods of Numerical Integration." Mathematical Gazette 70, no. 451 (March 1986): 70. http://dx.doi.org/10.2307/3615859.

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Дисертації з теми "Integration numerical"

Berry, Matthew M. "A Variable-Step Double-Integration Multi-Step Integrator." Diss., Virginia Tech, 2004. http://hdl.handle.net/10919/11155.

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A new method of numerical integration is presented here, the variable-step Stormer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms require a second evaluation. The variable-step Stormer-Cowell method is designed for space surveillance applications,which require numerical integration methods to track orbiting objects accurately. Because of the large number of objects being processed, methods that can integrate the equations of motion as fast as possible while maintaining accuracy requirements are desired. The force model used for earth-orbiting objects is quite complex and computationally expensive, so methods that minimize the force model evaluations are needed. The new method is compared to the fixed-step Gauss-Jackson method, as well as a method of analytic step regulation (s-integration), and the variable-step variable-order Shampine-Gordon integrator. Speed and accuracy tests of these methods indicate that the new method is comparable in speed and accuracy to s-integration in most cases, though the variable-step Stormer-Cowell method has an advantage over s-integration when drag is a significant factor. The new method is faster than the Shampine-Gordon integrator, because the Shampine-Gordon integrator uses two evaluations per step, and is biased toward keeping the step size constant. Tests indicate that both the new variable-step Stormer-Cowell method and s-integration have an advantage over the fixed-step Gauss-Jackson method for orbits with eccentricities greater than 0.15.
Ph. D.

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Lastdrager, Boris. "Numerical time integration on sparse grids." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2002. http://dare.uva.nl/document/64526.

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Ou, Rongfu. "Parallel numerical integration methods for nonlinear dynamics." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/18181.

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Akinola, Richard Olatokunbo. "Numerical indefinite integration using the sinc method." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/1049.

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Alsallami, Shami Ali M. "Discrete integrable systems and geometric numerical integration." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22291/.

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This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplectic schemes for Hamiltonian systems are accurate over long times. However, for nonlinear systems the series defining the modified Hamiltonian equation usually diverges. The first part of the thesis demonstrates that there are nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. Specifically, they arise as reductions of a lattice version of the Korteweg-de Vries (KdV) partial differential equation. We present cases of one and two degrees of freedom symplectic mappings, for which the modified Hamiltonian equations can be computed as a closed form expression using techniques of action-angle variables, separation of variables and finite-gap integration. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example is a system of an implicit dependence on the time step, which is obtained by dimensional reduction of a lattice version of the modified KdV equation. The second part of the thesis contains a different class of discrete-time system, namely the Boussinesq type, which can be considered as a higher-order counterpart of the KdV type. The development and analysis of this class by means of the B{\"a}cklund transformation, staircase reductions and Dubrovin equations forms one of the major parts of the thesis. First, we present a new derivation of the main equation, which is a nine-point lattice Boussinesq equation, from the B{\"a}cklund transformation for the continuous Boussinesq equation. Second, we focus on periodic reductions of the lattice equation and derive all necessary ingredients of the corresponding finite-dimensional models. Using the corresponding monodromy matrix and applying techniques from Lax pair and $r$-matrix structure analysis to the Boussinesq mappings, we study the dynamics in terms of the so-called Dubrovin equations for the separated variables.

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Strandberg, Rickard, and Johan Låås. "Uncertainty quantification using high-dimensional numerical integration." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-195701.

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We consider quantities that are uncertain because they depend on one or many uncertain parameters. If the uncertain parameters are stochastic the expected value of the quantity can be obtained by integrating the quantity over all the possible values these parameters can take and dividing the result by the volume of the parameter-space. Each additional uncertain parameter has to be integrated over; if the parameters are many, this give rise to high-dimensional integrals. This report offers an overview of the theory underpinning four numerical methods used to compute high-dimensional integrals: Newton-Cotes, Monte Carlo, Quasi-Monte Carlo, and sparse grid. The theory is then applied to the problem of computing the impact coordinates of a thrown ball by introducing uncertain parameters such as wind velocities into Newton’s equations of motion.

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Tranquilli, Paul J. "Lightly-Implicit Methods for the Time Integration of Large Applications." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/81974.

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Many scientific and engineering applications require the solution of large systems of initial value problems arising from method of lines discretization of partial differential equations. For systems with widely varying time scales, or with complex physical dynamics, implicit time integration schemes are preferred due to their superior stability properties. However, for very large systems accurate solution of the implicit terms can be impractical. For this reason approximations are widely used in the implementation of such methods. The primary focus of this work is on the development of novel ``lightly-implicit'' time integration methodologies. These methods consider the time integration and the solution of the implicit terms as a single computational process. We propose several classes of lightly-implicit methods that can be constructed to allow for different, specific approximations. Rosenbrock-Krylov and exponential-Krylov methods are designed to permit low accuracy Krylov based approximations of the implicit terms, while maintaining full order of convergence. These methods are matrix free, have low memory requirements, and are particularly well suited to parallel architectures. Linear stability analysis of K-methods is leveraged to construct implementation improvements for both Rosenbrock-Krylov and exponential-Krylov methods. Linearly-implicit Runge-Kutta-W methods are designed to permit arbitrary, time dependent, and stage varying approximations of the linear stiff dynamics of the initial value problem. The methods presented here are constructed with approximate matrix factorization in mind, though the framework is flexible and can be extended to many other approximations. The flexibility of lightly-implicit methods, and their ability to leverage computationally favorable approximations makes them an ideal alternative to standard explicit and implicit schemes for large parallel applications.
Ph. D.

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Qureshi, Muhammad Amer. "Efficient numerical integration for gravitational N-body simulations." Thesis, University of Auckland, 2012. http://hdl.handle.net/2292/10826.

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Models for N-body gravitational simulations of the Solar System vary from small simulations of two bodies over short intervals of time to simulations of large numbers of bodies over long-term integration. Most simulations require the numerical solution of an initial value problem (IVP) of second-order ordinary differential equation. We present new integration methods intended for accurate simulations that are more efficient than existing methods. In the first part of the thesis, we present new higher-order explicit Runge–Kutta Nyström pairs. These new pairs are searched using a simulated annealing algorithm based on optimisation. The new pairs are up to approximately 60% more efficient than the existing ones. We implement these new pairs for a variety of gravitational problems and investigate the growth of global error in position for these problems along with relative error in conserved quantities. The second part consists of the implementation of the Gauss Implicit Runge-Kutta methods in an efficient way such that the error growth satisfies Brouwer’s Law. Numerical experiments show that using the new way of implementation reduces the integration cost up to 20%. We also implement continuous extensions for the Gauss implicit Runge-Kutta methods, using interpolation polynomials at nodal points.

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Wang, Honghou 1963. "Practical adaptive numerical integration for finite element electromagnetics." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30277.

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Currently, several numerical methods have been provided for 2-D and 3-D integrations. But there is insufficient analysis reported on the overall performances of the available methods for fundamental electromagnetics problems. A complete evaluation is presented to discover the best ways of integrating these electromagnetics problems through benchmark performance studies of the available methods focussing on the integration accuracy, the location of sampling points, and the influence of integration domain refinement schemes. To meet this goal, three benchmark problems have been designed and evaluated. Accurate and reasonably cost-efficient integration methods are recommended.

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Oliva, Federico. "Modelling, stability, and control of DAE numerical integration." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20143/.

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This thesis deals with the integration of differential algebraic equations systems. Generally speaking the execution of numerical integration algorithms may introduce some errors, which could propagate ending up in a wrong description of system dynamics. This issue, named drifting, will be highlighted by dealing with a specific constrained mechanical system presenting. Such system consists of a looper, which is a mechanism used in the steel production to sense and control the tension acting on the material. The thesis unfolds as follows: a first section model the looper and inspects the main properties related to its joint space and singularities. A brief introduction to stability analysis on multidof systems is proposed. Then, the thesis proceeds analysing looper stability properties, eventually finding a globally asymptotic stable configuration. Lastly, the drifting is highlighted by numerical simulations. To solve this issue two control algorithms are proposed: the first is the Baumgarte algorithm and the second consists of a nonlinear stabilizer. A performance comparison of both algorithms is then presented at the end of the implementation description.

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Книги з теми "Integration numerical"

Keast, Patrick, and Graeme Fairweather, eds. Numerical Integration. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3889-2.

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Espelid, Terje O., and Alan Genz, eds. Numerical Integration. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2646-5.

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Evans, Gwynne. Practical numerical integration. Chichester: Wiley, 1993.

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Brass, H., and G. Hämmerlin, eds. Numerical Integration IV. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-6338-4.

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Braß, H., and G. Hämmerlin, eds. Numerical Integration III. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6398-8.

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Hairer, Ernst, Gerhard Wanner, and Christian Lubich. Geometric Numerical Integration. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-05018-7.

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Davis, Philip J. Methods of numerical integration. 2nd ed. Mineola, N.Y: Dover Publications, 2007.

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1946-, Ueberhuber Christoph W., ed. Computational integration. Philadelphia: Society for Industrial and Applied Mathematics, 1998.

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Handbook of integration. Boston: Jones and Bartlett, 1992.

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Introduction to integration. Oxford: Clarendon Press, 1997.

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Частини книг з теми "Integration numerical"

Johansson, Robert. "Integration." In Numerical Python, 267–93. Berkeley, CA: Apress, 2018. http://dx.doi.org/10.1007/978-1-4842-4246-9_8.

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Johansson, Robert. "Integration." In Numerical Python, 187–206. Berkeley, CA: Apress, 2015. http://dx.doi.org/10.1007/978-1-4842-0553-2_8.

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Hämmerlin, Günther, and Karl-Heinz Hoffman. "Integration." In Numerical Mathematics, 272–329. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4442-4_7.

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Komornik, Vilmos. "Numerical Integration." In Springer Undergraduate Mathematics Series, 231–66. London: Springer London, 2017. http://dx.doi.org/10.1007/978-1-4471-7316-8_10.

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Scherer, Philipp O. J. "Numerical Integration." In Graduate Texts in Physics, 45–57. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00401-3_4.

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Phillips, George M. "Numerical Integration." In CMS Books in Mathematics, 119–46. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21682-0_3.

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Gaul, Lothar, Martin Kögl, and Marcus Wagner. "Numerical Integration." In Boundary Element Methods for Engineers and Scientists, 175–204. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05136-8_6.

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Scherer, Philipp O. J. "Numerical Integration." In Graduate Texts in Physics, 47–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61088-7_4.

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Woodford, C., and C. Phillips. "Numerical Integration." In Numerical Methods with Worked Examples: Matlab Edition, 97–118. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_5.

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Stickler, Benjamin A., and Ewald Schachinger. "Numerical Integration." In Basic Concepts in Computational Physics, 29–50. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02435-6_3.

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Тези доповідей конференцій з теми "Integration numerical"

Luft, Brian, Vadim Shapiro, and Igor Tsukanov. "Geometrically adaptive numerical integration." In the 2008 ACM symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1364901.1364923.

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Milovanović, Gradimir V., Dobrilo e. Tošić, and Miloljub Albijanić. "Numerical integration of analytic functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756325.

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Savcenco, Valeriu, and Eugeniu Savcenco. "Multirate Numerical Integration for Parabolic PDEs." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990964.

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Yu Du. "Electromagnetic transient numerical integration methods." In 2010 8th World Congress on Intelligent Control and Automation (WCICA 2010). IEEE, 2010. http://dx.doi.org/10.1109/wcica.2010.5553948.

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Cerone, P., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Multidimensional Integration via Dimension Reduction and Generators." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790241.

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Ascher, Uri, and Kees van den Doel. "Fast but chaotic artificial time integration." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756678.

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Brugnano, Luigi, and Felice Iavernaro. "Geometric integration by playing with matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756051.

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Wensch, Jörg, Oswald Knoth, and Alexander Galant. "Multirate Time Integration for Compressible Atmospheric Flow." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991079.

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Walentyński, Ryszard A., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On Exact Integration Within an Isoparametric Tetragonal Finite Element." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790212.

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Zeng, Zhe-Zhao, Chen Ye, and Wei Zhu. "A New Method of Numerical Integration." In First International Conference on Innovative Computing, Information and Control. IEEE, 2006. http://dx.doi.org/10.1109/icicic.2006.390.

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Звіти організацій з теми "Integration numerical"

Lester, Brian T., and Kevin Nicholas Long. Numerical Integration of Viscoelastic Models. Office of Scientific and Technical Information (OSTI), September 2019. http://dx.doi.org/10.2172/1567985.

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Osborne, A. R. Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics. Fort Belvoir, VA: Defense Technical Information Center, September 2007. http://dx.doi.org/10.21236/ada578324.

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Allen, Christopher K. Preserving Simplecticity in the Numerical Integration of Linear Beam Optics. Office of Scientific and Technical Information (OSTI), July 2017. http://dx.doi.org/10.2172/1408583.

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Masalma, Yahya, and Yu Jiao. Technical Report: Scalable Parallel Algorithms for High Dimensional Numerical Integration. Office of Scientific and Technical Information (OSTI), October 2010. http://dx.doi.org/10.2172/990238.

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Zoller, Miklos. Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework. Office of Scientific and Technical Information (OSTI), July 2021. http://dx.doi.org/10.2172/1806423.

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Austin, M. High Order Integration of Smooth Dynamical Systems: Theory and Numerical Experiments. Fort Belvoir, VA: Defense Technical Information Center, January 1991. http://dx.doi.org/10.21236/ada445569.

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Robinson, Eric. Comparing Three Types of Numerical Techniques for the Integration of Perturbed Satellite Motion. Office of Scientific and Technical Information (OSTI), June 2010. http://dx.doi.org/10.2172/1117981.

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Judd, Kenneth L., and Ben Skrainka. High performance quadrature rules: how numerical integration affects a popular model of product differentiation. Institute for Fiscal Studies, February 2011. http://dx.doi.org/10.1920/wp.cem.2011.0311.

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Bammann, Douglas J., G. C. Johnson, Esteban B. Marin, and Richard A. Regueiro. On the formulation, parameter identification and numerical integration of the EMMI model :plasticity and isotropic damage. Office of Scientific and Technical Information (OSTI), January 2006. http://dx.doi.org/10.2172/883488.

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Osborne, A. R. Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada612395.

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