Numerical Solution of Three-Dimensional Time-Space Fractional Order Reaction–Advection–Diffusion Equation by Shifted Legendre–Gauss–Lobatto Collocation Method

Abstract

In the present article, a shifted Legendre–Gauss–Lobatto collocation method (SLGLCM) is introduced to derive an approximate solution for a three-dimensional time-space fractional order reaction–advection–diffusion equation (3D-TSFRADE) with initial and boundary conditions. The proposed method involves reducing the 3D-TSFRADE into a system of algebraic equations, which has been solved by applying Newton method. Two examples are provided to illustrate the accuracy and efficiency of the proposed method through error analysis between the numerical and exact solutions. © 2025 John Wiley & Sons Ltd.