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

TL;DR

This paper introduces a new non-polynomial quintic spline method combined with finite difference for solving fourth-order time fractional PDEs, demonstrating improved accuracy and stability over existing methods.

Contribution

The paper develops a novel non-polynomial quintic spline approach for space discretization in fractional PDEs, enhancing accuracy and stability compared to traditional methods.

Findings

The scheme is proven to be stable and convergent.

Numerical results show higher accuracy than existing methods.

The method effectively solves test problems with improved precision.

Abstract

This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). 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.