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Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

F. Kadhem, Mohanad, and Ali H. Alfayadh. "Mixed Homotopy Integral Transform Method for Solving Non-Linear ntegro-Differential Equation." Al-Nahrain Journal of Science 25, no. 1 (March 1, 2022): 35–40. http://dx.doi.org/10.22401/anjs.25.1.06.

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In this paper, we have applied Sawi transform with homotopyperturbation method to obtain analytic approximation for non-linear integro-differential Equations. The proposed technique is compared with homotopy perturbation method and Abood transform homotopy perturbation method. The results show that Sawi transform homotopy perturbation is an efficient approach to solve non-linear integro-differential equations.

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2

Journal, Baghdad Science. "An approximate solution for solving linear system of integral equation with application on "Stiff" problems." Baghdad Science Journal 2, no. 1 (March 6, 2005): 148–54. http://dx.doi.org/10.21123/bsj.2.1.148-154.

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3

DERMOUNE, Azzouz. "Non-commutative Burgers equation." Hokkaido Mathematical Journal 25, no. 2 (February 1996): 315–32. http://dx.doi.org/10.14492/hokmj/1351516727.

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4

Kremp, D., M. Bonitz, W. D. Kraeft, and M. Schlanges. "Non-Markovian Boltzmann Equation." Annals of Physics 258, no. 2 (August 1997): 320–59. http://dx.doi.org/10.1006/aphy.1997.5703.

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5

Shushin, A. I., and V. P. Sakun. "Non-Markovian stochastic Liouville equation." Physica A: Statistical Mechanics and its Applications 340, no. 1-3 (September 2004): 283–91. http://dx.doi.org/10.1016/j.physa.2004.04.018.

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6

Munro, W. J., and C. W. Gardiner. "Non-rotating-wave master equation." Physical Review A 53, no. 4 (April 1, 1996): 2633–40. http://dx.doi.org/10.1103/physreva.53.2633.

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7

Das, Amal K. "A non‐Fickian diffusion equation." Journal of Applied Physics 70, no. 3 (August 1991): 1355–58. http://dx.doi.org/10.1063/1.349592.

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8

Gaspard, P., and M. Nagaoka. "Non-Markovian stochastic Schrödinger equation." Journal of Chemical Physics 111, no. 13 (October 1999): 5676–90. http://dx.doi.org/10.1063/1.479868.

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9

Alexanian, Moorad. "Classical non-Markovian Boltzmann equation." Journal of Mathematical Physics 55, no. 8 (August 2014): 083301. http://dx.doi.org/10.1063/1.4886475.

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10

Doliwa, Adam. "Non-commutativeq-Painlevé VI equation." Journal of Physics A: Mathematical and Theoretical 47, no. 3 (December 23, 2013): 035203. http://dx.doi.org/10.1088/1751-8113/47/3/035203.

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11

Shadman, Dariush, and Bahman Mehri. "A non-homogeneous Hill’s equation." Applied Mathematics and Computation 167, no. 1 (August 2005): 68–75. http://dx.doi.org/10.1016/j.amc.2004.06.072.

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12

Thomson, Mark J., and Bruce H. J. McKellar. "The non-linear MSW equation." Physics Letters B 259, no. 1-2 (April 1991): 113–18. http://dx.doi.org/10.1016/0370-2693(91)90143-e.

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13

Kochubei, Anatoly. "A non-Archimedean wave equation." Pacific Journal of Mathematics 235, no. 2 (April 1, 2008): 245–61. http://dx.doi.org/10.2140/pjm.2008.235.245.

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14

OBERLACK, MARTIN. "Non-isotropic dissipation in non-homogeneous turbulence." Journal of Fluid Mechanics 350 (November 10, 1997): 351–74. http://dx.doi.org/10.1017/s002211209700712x.

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On the basis of the two-point velocity correlation equation a new tensor length-scale equation and in turn a dissipation rate tensor equation and the pressure–strain correlation are derived by means of asymptotic analysis and frame-invariance considerations. The new dissipation rate tensor equation can account for non-isotropy effects of the dissipation rate and streamline curvature. The entire analysis is valid for incompressible as well as for compressible turbulence in the limit of small Mach numbers. The pressure–strain correlation is expressed as a functional of the two-point correlation, leading to an extended compressible version of the linear formulation of the pressure–strain correlation. In this turbulence modelling approach the only terms which still need ad hoc closure assumptions are the triple correlation of the fluctuating velocities and a tensor relation between the length scale and the dissipation rate tensor. Hence, a consistent formulation of the return term in the pressure–strain correlation and the dissipation tensor equation is achieved. The model has been integrated numerically for several different homogeneous and inhomogeneous test cases and results are compared with DNS, LES and experimental data.

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15

Escher, Joachim, and Boris Kolev. "The Degasperis–Procesi equation as a non-metric Euler equation." Mathematische Zeitschrift 269, no. 3-4 (September 28, 2010): 1137–53. http://dx.doi.org/10.1007/s00209-010-0778-2.

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16

Malham, Simon J. A. "Integrability of local and non-local non-commutative fourth-order quintic non-linear Schrödinger equations." IMA Journal of Applied Mathematics 87, no. 2 (March 17, 2022): 231–59. http://dx.doi.org/10.1093/imamat/hxac002.

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Abstract We prove integrability of a generalized non-commutative fourth-order quintic non-linear Schrödinger equation. The proof is relatively succinct and rooted in the linearization method pioneered by Ch. Pöppe. It is based on solving the corresponding linearized partial differential system to generate an evolutionary Hankel operator for the ‘scattering data’. The time-evolutionary solution to the non-commutative non-linear partial differential system is then generated by solving a linear Fredholm equation which corresponds to the Marchenko equation. The integrability of reverse space-time and reverse time non-local versions, in the sense of Ablowitz and Musslimani (2017, Integrable nonlocal nonlinear equations, Stud. Appl. Math. 139, 7–59), of the fourth-order quintic non-linear Schrödinger equation are proved contiguously by the approach adopted. Further, we implement a numerical integration scheme based on the analytical approach above, which involves solving the linearized partial differential system followed by numerically solving the linear Fredholm equation to generate the solution at any given time.

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17

Badiale, M., and G. Cappa. "Non radial solutions for a non homogeneous Hénon equation." Nonlinear Analysis: Theory, Methods & Applications 109 (November 2014): 45–55. http://dx.doi.org/10.1016/j.na.2014.06.020.

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18

Terraneo, Elide. "NON-UNIQUENESS FOR A CRITICAL NON-LINEAR HEAT EQUATION." Communications in Partial Differential Equations 27, no. 1-2 (November 3, 2002): 185–218. http://dx.doi.org/10.1081/pde-120002786.

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19

Bisconti, Luca, and Matteo Franca. "On a non-homogeneous and non-linear heat equation." Dynamics of Partial Differential Equations 12, no. 4 (2015): 289–320. http://dx.doi.org/10.4310/dpde.2015.v12.n4.a1.

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20

Felmer, Patricio, and César Torres. "Non-linear Schrödinger equation with non-local regional diffusion." Calculus of Variations and Partial Differential Equations 54, no. 1 (September 23, 2014): 75–98. http://dx.doi.org/10.1007/s00526-014-0778-x.

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21

Simons, Stuart. "93.50 A non-linear difference equation." Mathematical Gazette 93, no. 528 (November 2009): 500–504. http://dx.doi.org/10.1017/s0025557200185298.

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22

Cruse, T. A., and R. Aithal. "Non-singular boundary integral equation implementation." International Journal for Numerical Methods in Engineering 36, no. 2 (January 30, 1993): 237–54. http://dx.doi.org/10.1002/nme.1620360205.

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23

Caffarelli, Luis, and Luis Silvestre. "A non-local Monge–Ampère equation." Communications in Analysis and Geometry 24, no. 2 (2016): 307–35. http://dx.doi.org/10.4310/cag.2016.v24.n2.a4.

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24

Qiu, Yan, and Jens Lorenz. "A non-linear Black-Scholes equation." International Journal of Business Performance and Supply Chain Modelling 1, no. 1 (2009): 33. http://dx.doi.org/10.1504/ijbpscm.2009.026264.

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25

FORMIGA, J. B., and C. ROMERO. "DIRAC EQUATION IN NON-RIEMANNIAN GEOMETRIES." International Journal of Geometric Methods in Modern Physics 10, no. 07 (June 10, 2013): 1320012. http://dx.doi.org/10.1142/s0219887813200120.

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We present the Dirac equation in a geometry with torsion and non-metricity balancing generality and simplicity as much as possible. In doing so, we use the vielbein formalism and the Clifford algebra. We also use an index-free formalism which allows us to construct objects that are totally invariant. It turns out that the previous apparatuses not only make possible a simple deduction of the Dirac equation but also allow us to exhibit some details that is generally obscure in the literature.

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26

Yang, Xiaofan, David J. Evans, and Graham M. Megson. "On a non-autonomous difference equation." Applied Mathematics and Computation 168, no. 1 (September 2005): 380–88. http://dx.doi.org/10.1016/j.amc.2004.09.004.

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27

Vlasiou, Maria. "A non-increasing Lindley-type equation." Queueing Systems 56, no. 1 (May 23, 2007): 41–52. http://dx.doi.org/10.1007/s11134-007-9029-6.

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28

Wu, N. S., and W. Wei. "Empirical equation for relative non-overlap." Chromatographia 35, no. 7-8 (April 1993): 471. http://dx.doi.org/10.1007/bf02278606.

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29

Pourdarvish, A., J. Sadeghi, and N. J. Hassan. "The position non Markovian master equation." Chaos, Solitons & Fractals 95 (February 2017): 57–64. http://dx.doi.org/10.1016/j.chaos.2016.12.016.

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30

Awawdeh, A., and M. Aloqeili. "Dynamics of non-autonomous difference equation." Journal of Applied Mathematics and Computing 55, no. 1-2 (July 7, 2016): 279–91. http://dx.doi.org/10.1007/s12190-016-1036-5.

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31

Wu, N. S., and W. Wei. "Empirical equation for relative non-overlap." Chromatographia 34, no. 9-10 (November 1992): 450–52. http://dx.doi.org/10.1007/bf02290234.

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32

Ares de Parga, G., S. Domínguez-Hernández, and E. Salinas-Hernández. "Non relativistic limit of the Landau–Lifshitz equation: A new equation." Annals of Physics 369 (June 2016): 45–65. http://dx.doi.org/10.1016/j.aop.2016.02.012.

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33

Zhang, Sheng, and Xiaowei Zheng. "Non-differentiable solutions for non-linear local fractional heat conduction equation." Thermal Science 25, Spec. issue 2 (2021): 309–14. http://dx.doi.org/10.2298/tsci21s2309z.

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Fractional calculus has many advantages. Under consideration of this paper is a (2+1)-dimensional non-linear local fractional heat conduction equation with arbitrary degree non-linearity. Backlund transformation of a reduced form of the local fractional heat conduction equation is constructed by Painleve analysis. Based on the Backlund transformation, some exact non-differentiable solutions of the local fractional heat conduction equation are obtained. To gain more insights of the obtained solutions, two solutions are constrained to a Cantor set and then two spatio-temporal fractal structures with profiles of these two solutions are shown. This paper further reveals by local fractional heat conduction equation that fractional calculus plays important role in dealing with non-differentiable problems.

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34

Bödeker, Dietrich. "Perturbative and non-perturbative aspects non-Abelian Boltzmann–Langevin equation." Nuclear Physics B 647, no. 3 (December 2002): 512–38. http://dx.doi.org/10.1016/s0550-3213(02)00841-6.

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35

Macías-Díaz, Jorge E., María G. Medina-Guevara, and Héctor Vargas-Rodríguez. "Exact solutions of non-linear Klein–Gordon equation with non-constant coefficients through the trial equation method." Journal of Mathematical Chemistry 59, no. 3 (February 26, 2021): 827–39. http://dx.doi.org/10.1007/s10910-021-01220-y.

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36

Haouam, Ilyas. "The Non-Relativistic Limit of the DKP Equation in Non-Commutative Phase-Space." Symmetry 11, no. 2 (February 14, 2019): 223. http://dx.doi.org/10.3390/sym11020223.

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The non-relativistic limit of the relativistic DKP equation for both of zero and unity spin particles is studied through the canonical transformation known as the Foldy–Wouthuysen transformation, similar to that of the case of the Dirac equation for spin-1/2 particles. By considering only the non-commutativity in phases with a non-interacting fields case leads to the non-commutative Schrödinger equation; thereafter, considering the non-commutativity in phase and space with an external electromagnetic field thus leads to extract a phase-space non-commutative Schrödinger–Pauli equation; there, we examined the effect of the non-commutativity in phase-space on the non-relativistic limit of the DKP equation. However, with both Bopp–Shift linear transformation through the Heisenberg-like commutation relations, and the Moyal–Weyl product, we introduced the non-commutativity in phase and space.

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37

Rom, Celina. "A version of non-Hamiltonian Liouville equation." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 34, no. 1 (2014): 5. http://dx.doi.org/10.7151/dmdico.1158.

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38

Bonnefon, Olivier, Jérôme Coville, and Guillaume Legendre. "Concentration phenomenon in some non-local equation." Discrete & Continuous Dynamical Systems - B 22, no. 3 (2017): 763–81. http://dx.doi.org/10.3934/dcdsb.2017037.

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39

Zhang, Xiaomin, Song Peng, Long Zhang, Zimin Yan, Yuan Liang, and Bo Yan. "VARIATIONAL EQUATION OF NON-FOURIER HEAT CONDUCTION." Heat Transfer Research 49, no. 3 (2018): 275–85. http://dx.doi.org/10.1615/heattransres.2018015988.

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40

Jia, Houyu, and Liya Jiang. "On non-linear elliptic equation with weight." Nonlinear Analysis: Theory, Methods & Applications 61, no. 3 (May 2005): 477–83. http://dx.doi.org/10.1016/j.na.2004.12.007.

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41

Lenzi, E. K., L. R. Evangelista, M. K. Lenzi, H. V. Ribeiro, and E. C. de Oliveira. "Solutions for a non-Markovian diffusion equation." Physics Letters A 374, no. 41 (September 2010): 4193–98. http://dx.doi.org/10.1016/j.physleta.2010.08.049.

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42

Tasso, H. "A non-linear equation for drift waves." Physics Letters A 232, no. 3-4 (July 1997): 247–51. http://dx.doi.org/10.1016/s0375-9601(97)00367-8.

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43

CLIMENHAGA, VAUGHN. "Bowen’s equation in the non-uniform setting." Ergodic Theory and Dynamical Systems 31, no. 4 (July 20, 2010): 1163–82. http://dx.doi.org/10.1017/s0143385710000362.

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AbstractWe show that Bowen’s equation, which characterizes the Hausdorff dimension of certain sets in terms of the topological pressure of an expanding conformal map, applies in greater generality than has been heretofore established. In particular, we consider an arbitrary subset Z of a compact metric space and require only that the lower Lyapunov exponents be positive on Z, together with a tempered contraction condition. Among other things, this allows us to compute the dimension spectrum for Lyapunov exponents for maps with parabolic periodic points, and to relate the Hausdorff dimension to the topological entropy for arbitrary subsets of symbolic space with the appropriate metric.

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44

Pozo, Juan C., and Vicente Vergara. "A non-local in time telegraph equation." Nonlinear Analysis 193 (April 2020): 111411. http://dx.doi.org/10.1016/j.na.2019.01.001.

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45

Govinder, K. S., and P. G. L. Leach. "SOLUTION OF THE NON-LINEAR DIFFERENTIAL EQUATION." Transactions of the Royal Society of South Africa 49, no. 2 (January 1994): 175–84. http://dx.doi.org/10.1080/00359199409520305.

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46

Marconi, Umberto Marini Bettolo, Simone Melchionna, and Ignacio Pagonabarraga. "Effective electrodiffusion equation for non-uniform nanochannels." Journal of Chemical Physics 138, no. 24 (June 28, 2013): 244107. http://dx.doi.org/10.1063/1.4811516.

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47

Bakery, Awad A., and Afaf R. Abou Elmatty. "Non Linear Difference Equation of Orlicz Type." Journal of Computational and Theoretical Nanoscience 14, no. 1 (January 1, 2017): 306–13. http://dx.doi.org/10.1166/jctn.2017.6321.

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We give here the sufficient conditions on the positive solutions of the difference equation xn+1 = α+M((xn−1)/xn), n = 0, 1, …, where M is an Orlicz function, α∈ (0, ∞) with arbitrary positive initials x−1, x0 to be bounded, α-convergent and the equilibrium point to be globally asymptotically stable. Finally we present the condition for which every positive solution converges to a prime two periodic solution. Our results coincide with that known for the cases M(x) = x in Ref. [3] and M(x) = xk, where k ∈ (0, ∞) in Ref. [7]. We have given the solution of open problem proposed in Ref. [7] about the existence of the positive solution which eventually alternates above and below equilibrium and converges to the equilibrium point. Some numerical examples with figures will be given to show our results.

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48

Nayak, G. C. "Altarelli-parisi equation in non-equilibrium QCD." Physics of Particles and Nuclei 43, no. 6 (November 2012): 742–48. http://dx.doi.org/10.1134/s106377961206007x.

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49

Oh, Eunjin. "Locus equation parameters in non‐native speech." Journal of the Acoustical Society of America 107, no. 5 (May 2000): 2803. http://dx.doi.org/10.1121/1.429027.

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50

Biró, Tamás S., and Gábor Purcsel. "Numerical Simulation of Non-Extensive Boltzmann Equation." Acta Physica Hungarica A) Heavy Ion Physics 27, no. 2-3 (October 1, 2006): 367–71. http://dx.doi.org/10.1556/aph.27.2006.2-3.42.

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