Novel Computational Methods Based on Shifted Jacobi Operational Matrix for Space Fractional Diffusion Equation

Abstract

This article investigates the space fractional diffusion equation (SFDE). In this work, two efficient and precise numerical methods (Novel Shifted Jacobi Operational Matrix techniques) are applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of these schemes is their ability to transform linear and nonlinear (PDE)s into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested techniques are effectively utilized for the aforementioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the techniques introduced. To demonstrate the effectiveness and accuracy of these techniques, the numerical results from the examples are presented in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the implementation of the current methods are considered very easy and general for many numerical techniques.