Non-Polynomial Quintic Spline for Numerical Solution of Fourth--Order Time Fractional Partial Differential Equations
Provides a more accurate numerical scheme for solving a specific class of fractional PDEs, but the improvement is incremental.
The paper develops a non-polynomial quintic spline method combined with finite differences for solving fourth-order time-fractional PDEs, demonstrating improved accuracy over existing methods through test problems.
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.