Affiliation:
1. School of Mathematics Iran University of Science and Technology Narmak Tehran Iran
2. Department of Mathematics and Computer Science Brandon University Brandon Manitoba Canada
Abstract
AbstractWe study the two‐dimensional stochastic time‐fractional Sine–Gordon equation (2D ST‐FS‐G) and provide a solution for it. We use the new clique polynomial method to obtain a numerical solution to the 2D TFS‐G equation. In this technique, the clique polynomial is considered as a basic function for operational matrices. By converting the 2D ST‐FS‐G equation to algebraic equations, a solution is obtained for the desired equation, which clearly shows that this approach is suitable and accurate for dealing with the equation. We further present the error boundary for the obtained approximation of the desired three‐variable function based on the clique polynomial. Finally, we compare some numerical results obtained with the exact ones by a few practical examples.
Subject
Electrical and Electronic Engineering,Computer Science Applications,Modeling and Simulation
Reference42 articles.
1. Haar wavelet method for solving fractional partial differential equations numerically;Wang L;Appl Math Comput,2014
2. Fractional Calculus and Waves in Linear Viscoelasticity
3. A piecewise linear FEM for an optimal control problem of fractional operators: error analysis on curved domains;Otarola E;ESAIM Math Model Numer Anal,2017
4. Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations
5. A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations