On the Numerical Solution of Widely Used 2D Stochastic Partial‎ ‎Differential‎ ‎Equation in Representing‎ ‎Reaction-Diffusion Processes

In this paper, a combined methodology based on the method of lines (MOL) and spline is implemented to simulate the solution of a two-dimensional (2D) stochastic fractional telegraph equation with Caputo fractional derivatives of order α and β where 1 < α, β ≤ 2. In this approach, the spatial directions are discretized by selecting some equidistance mesh points. Then fractional derivatives are estimated via linear spline approximation and some finite difference formulas. After substituting these estimations in the semi-discretization equation, the considered problem is transformed into a system of second-order initial value problems (IVPs), which is solved by using an ordinary differential equations (ODEs) solver technique in Matlab software. Also, it is proved that the rate of convergence is O(∆x2 + ∆y2), where ∆x and ∆y denote the spatial step size in x and y directions, respectively. Finally, two examples are included to confirm the efficiency of the suggested method.