Non-Polynomial Quintic Spline for Numerical Solution of Fourth-Order Time Fractional Partial Differential Equations

Abstract

This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.