An Efficient Solution for Stochastic Fractional Partial Differential Equations with Additive Noise by a Meshless Method

An Efficient Solution for Stochastic Fractional Partial Differential Equations with Additive... With respect to wide range of applications of stochstic partial differential equation (SPDE) and high ability of meshless methods to solve complicated problems, in this paper, an efficient numerical method for the time fractional SPDE, formulated with Caputo’s fractional derivative, based on meshless methods is presented. This article presents a meshless method based on the radial basis functions to solve one-dimensional stochastic heat and advection–diffusion equations. In here, first, we approximate the time fractional derivative of the mentioned equations by a scheme of order $$ \mathsf {O}(\tau ^{2-\alpha }) $$ O ( τ 2 - α ) , $$ 0<\alpha <1 $$ 0 < α < 1 then the spatial derivatives are approximated by Kansa approach. Numerical examples are presented to show the efficiency and effectiveness of the proposed method in solving fractional SPDEs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Applied and Computational Mathematics Springer Journals

An Efficient Solution for Stochastic Fractional Partial Differential Equations with Additive Noise by a Meshless Method

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer (India) Private Ltd., part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Mathematical Modeling and Industrial Mathematics; Operations Research/Decision Theory; Theoretical, Mathematical and Computational Physics; Computational Science and Engineering; Nuclear Energy
ISSN
2349-5103
eISSN
2199-5796
D.O.I.
10.1007/s40819-017-0455-9
Publisher site
See Article on Publisher Site

Abstract

With respect to wide range of applications of stochstic partial differential equation (SPDE) and high ability of meshless methods to solve complicated problems, in this paper, an efficient numerical method for the time fractional SPDE, formulated with Caputo’s fractional derivative, based on meshless methods is presented. This article presents a meshless method based on the radial basis functions to solve one-dimensional stochastic heat and advection–diffusion equations. In here, first, we approximate the time fractional derivative of the mentioned equations by a scheme of order $$ \mathsf {O}(\tau ^{2-\alpha }) $$ O ( τ 2 - α ) , $$ 0<\alpha <1 $$ 0 < α < 1 then the spatial derivatives are approximated by Kansa approach. Numerical examples are presented to show the efficiency and effectiveness of the proposed method in solving fractional SPDEs.

Journal

International Journal of Applied and Computational MathematicsSpringer Journals

Published: Nov 29, 2017

References

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