In this paper, first, the fuzzy Poisson’s equation and the fuzzy finite difference method are introduced. Then, the fuzzy Poisson’s equation is discretized by fuzzy finite difference method and it is solved as a linear system of equations. In addition, we discuss fuzzy Laplace equation as a special case of fuzzy Poisson’s equation. Finally, the convergence of method is taken into account and for more illustration a numerrical example is solved.
AlikhaniR. and BahramiF., Fuzzy partial differential equations under the cross product of fuzzy numbers, Information Science494 (2019), 80–99.
2.
AlikhaniR., BahramiF. and ParviziS., Differential calculus of fuzzy multi-variable functions and its applications to fuzzy partial differential equations, Fuzzy Sets and Systemes. https://doi.org/10.1016/j.fss.2019.04.011
3.
AllahviranlooT., Difference methods for fuzzy partial differential equations, Computational Methods in Applied Mathematics2(3) (2002), 233–242.
4.
AllahviranlooT., GhanbariM., HosseinzadehA.A., HaghiE. and NuraeiR., A note on “Fuzzy linear systems”, Fuzzy Sets and Systems177 (2011), 87–92.
5.
BarrosL.C. and PedroF.S., Fuzzy differential equations with interactive derivative, Fuzzy Sets and Systemes309 (2017), 64–80.
6.
BedeB. and StefanianiL., Generalized differentiability of fuzzy-valued functions, Fuzzy Sets and Systemes230 (2013), 119–141.
7.
BuckleyJ.J. and FeuringT., Introduction to fuzzy partial differential equation, Fuzzy Sets and Systems105 (1999), 241–248.
8.
BuzbeeB.L., DorrF.W., GeorgeJ.A. and GolubG.H., The direct solution of the discrete poisson equation on irregular regions, SIAM Journal on Numerical Analysis4 (1971), 722–736.
9.
ChangS.L. and ZadehL.A., On fuzzy mapping and control, IEEE Trans Systems Man Cyberent2 (1972), 30–34.
10.
DuboisD. and PradeH., Towards fuzzy differential calculus: Part 3, Differentiation Fuzzy Sets and Systems8 (1982), 225–233.
11.
ForsytheG.E. and WasowW.R., Finite difference method for partial differential equations, John Wiley, New york, 1960.
12.
Ghasemi MoghaddamR. and AllahviranlooT., On the fuzzy poisson equation, Fuzzy Sets and Systemes347 (2018), 105–128.
13.
GouyandehZ., AllahviranlooT., AbbasbandyS. and ArmandA., A fuzzy solution of heat equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets and Systemes309 (2017), 81–97.
14.
HosseinverdiS. and FaselH., An effcient, high-order method for solving Poisson equation for immersed boundaries: Combination of compact difference and multiscale multigrid methods, Journal of Computational Physics374 (2018), 912–940.
15.
IbanezD.S., BarrosL.C. and EsmiE., On interactive fuzzy boundary value problems, Fuzzy Sets and Systemes358 (2019), 84–96.
16.
KhastanA., New solutions for first order linear fuzzy difference equations, Journal of Computational and Applied Mathematics312 (2017), 156–166.
17.
KhastanA. and LopezR., On linear fuzzy differential equations by differential inclusions’ approach, Fuzzy Sets and Systemes, https://doi.org/10.1016/j.fss.2019.05.014
18.
LuT. and ShiouS., Inverses of 2×2 block matrices, Computers and Mathematics with Applications43 (2002), 119–129.
19.
MondalS., Interval-valued fuzzy vector space, Annals of Pure and Applied Mathematics2(1) (2012), 86–95.
20.
SereshN.G. and FayekA.R., Computational method for fuzzy arithmetic operations on triangular fuzzy numbers by extension principle, International Journal of Approximate Reasoning106 (2019), 172–193.
21.
StefaniniL. and BedeB., Generalized Hukuhara differentiability of interval-valued functions and interval differential equations, Nonlinear Analysis: Theory, Methods Applications71 (2009), 1311–1328.