Numerical solutions for a class stochastic partial differential equations

Document Type : Research Paper

Authors

Deparment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

Abstract

The aim of this manuscript is to introduce and analyze a stochastic finite difference  scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed  stochastic finite difference scheme show the efficiency of the suggested  stochastic finite difference scheme.

Keywords

Main Subjects

References

[1] Allen, E.J., Novose, S.J., & Zhang, Z.C. (1998). Finite element and di erence approximation of some linear stochastic partial di erential equations, Stochastic Rep. vol 64, 117{142. https://doi.org/10.1080/17442509808834159
[2] Baleanu, D., Namjoo, M., Mohebbian, A., & Jajarmi, A. (2022) A Weighted average  nite di erence scheme for the numerical solution of stochastic parabolic partial di erential equations, CMES - Comput. Model. Eng. Sci. 135(2), 1147{1163. https://doi.org/10.32604/cmes.2022.022403
[3] Bishehniasar, M., & Soheili, A. R. (2013) Approximation of stochastic advection diffusion equation using compact  nite di erence technique, Iran J. Sci. Technol. 37A3, 327{333. https://doi.org/10.22099/ijsts.2013.1631
[4] Iqbal, S., Martnez, F., Kaabar, M. K. A, & Samei, M. E. (2022) A novel Elzaki transform homotopy perturbation method for solving time-fractional non-linear partial differential equations, Bound. Value Probl. 2022(1), 91. https://doi.org/10.1186/s13661-022-01673-3
[5] Kamrani, M., & Hosseini, S. M. (2021) Spectral collocation method for stochastic burgers equation driven by additive noise, Math. Comput. Simul. 82, 1630{1644. https://doi.org/10.1016/j.matcom.2012.03.007
[6] Kaur, N., & Goyal, K. (2022) An adaptive wavelet optimized  nite di erence B-spline polynomial chaos method for random partial di erential equations, Appl. Math. Comput. 415, 126738. https://doi.org/10.1016/j.amc.2021.126738
[7] Kloeden, P. E., & Platen, E. (1995) Numerical Solution of Stochastic Di erential Equations, Springer. Berlin. https://doi.org/10.1007/978-3-662-12616-5
[8] Mirzaee, F., & Samadyar, N. (2020) Combination of  nite di erence method and meshless method based on radial basis functions to solve fractional stochastic advection{ di usion equations, Eng. Comput. 36, 1673{1686.  https://doi.org/10.1007/s00366-019-00789-y
[9] Namjoo, M., & Mohebbian, A. (2016) Approximation of stochastic advection diffusion equations with  nite di erence scheme, J. Math. Model. 4(1), 1{18.  https://jmm.guilan.ac.ir/article 1571.html
[10] Namjoo, M., & Mohebbian, A. (2019) Analysis of the stability and convergence of a  nite di erence approximation for stochastic partial di erential equations, Comput. Methods Di er. Equ. 7(3), 334{358. https://dorl.net/dor/20.1001.1.23453982.2019.7.3.2.8
[11] Roth, C. (2002) Di erence methods for stochastic partial di erential equations, Z. Zngew. Math. Mech 82, 821{830. https://doi.org/10.1002/1521-4001(200211)82:11/12<821::AID-ZAMM821>3.0.CO;2-L
[12] Soheili, A. R., & Arezoomandan, M. (2013) Approximation of stochastic advection di u-sion equations with stochastic alternative direction explicit methods, Appl. Math. 58(4),439{471. https://doi.org/10.1007/s10492-013-0022-6
[13] Walsh, J. B. (2005) Finite element methods for parabolic stochastic PDEs, Potential Anal. 23, 1{43. https://doi.org/10.1007/s11118-004-2950-y
[14] Yasin, M. W., Iqbal, M. S., Ahmed, N., Akgul, A., Raza, A., Ra q, M., & Riaz, M. B. (2022) Numerical scheme and stability analysis of stochastic Fitzhugh-Nagumo model, Results Phys. 32, 105023. https://doi.org/10.1016/j.rinp.2021.105023
[15] Yoo, H. (1999) Semi-discretization of stochastic partial di erential equation on R by a  nite di erence method, Math. Comp. 69, 653{666. https://www.jstor.org/stable/2584895
[16] Youssri, Y. H.,& Muttardi, M. M. (2023) A mingled tau- nite di erence method for stochastic  rst-order partial di erential equations, Int. J. Appl. Comput. 9, 1{14. https://doi.org/10.1007/s40819-023-01489-4
Journal of Mahani Mathematical Research
Volume 13, Issue 1 - Serial Number 26
November 2023
Pages 357-382

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History

  • Receive Date: 11 April 2023
  • Revise Date: 03 August 2023
  • Accept Date: 29 September 2023

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