Meshless local numerical procedure based on interpolating moving least squares approximation and exponential time differencing fourth-order Runge–Kutta (ETDRK4) for solving stochastic parabolic interface problems

Abstract

The main propose of this investigation is to develop an interpolating meshless numerical procedure for solving the stochastic parabolic interface problems. The present numerical algorithm is constructed from the interpolating moving least squares (ISMLS) approximation. At first, the space variable has been discretized by using the ISMLS approximation. Then, the PDE reduces to the system of nonlinear ODEs. In the next, to achieve a high-order numerical formula, we employ a fourth-order time discrete scheme that is well-known as the explicit fourth-order exponential time differencing Runge-Kutta method (ETDRK4). This method is simple and has acceptable accuracy for solving the considered problems. Several examples with adequate intricacy are examined to check the new numerical procedure.