A novel stochastic ten non-polynomial cubic splines method for heat equations with noise term

Abstract

In this paper, a new numerical method for solving a class of stochastic partial differential equations is presented. The proposed method is based on a non-polynomial cubic spline algorithm with an O(h4) local truncation error. The new approach has the advantage of simultaneously including ten non-polynomial cubic spline schemes. The proposed approach is also tested on three stochastic heat equations. The current results are compared to solutions obtained using the B-spline wavelet approximation method. The provided solutions demonstrate the proposed method's accuracy and applicability.