Crank Nicolson Approximation to Space-Time Fractional Stochastic Traveling Wave Equation with additive white noise

Abstract

ABSTRACT: This article describes a Crank-Nicolson finite difference approach for numerically predict-
ing the solutions of space- time fractional stochastic traveling wave equation (STFSTWE) with additive
white noise. The model employs a right-shifted Grunwald fractional derivative in the spatial dimen-
sion and a Caputo-type fractional derivative in the time dimension for discretization. The fractional
orders for space and time ranges from 1 < α ≤ 2 and 1 < β ≤ 2 respectively. The proposed numerical
technique discretizes the governing equations into a nonlinear algebraic system at each time level with
the coefficient matrix generated systematically using an automated procedure. Python gives graphical
representations of the answers in numerous situations, establishing the method’s efficiency. Furthermore,
two numerical experiments are included to validate the numerical approach. Stability and convergence
are also investigated using the mean square method.