2024/10/30 by Anthony Anya Okeke, Nur Nadiah Abd Hamid, Wen Eng Ong +1 · 1 voice
Mathematics · #Differential Equations and Numerical Methods #Fractional Differential Equations Solutions #Numerical methods for differential equations
paper · pdf · doi:10.46481/jnsps.2025.2323
openalex publication_date 2024/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
In this research, we develop an innovative and efficient numerical method for solving a nonlinear one-dimensional time-fractional convection-diffusion-reaction equation (TFCDRE) with a variable coefficient. This method integrates the Crank-Nicolson finite difference scheme with extended cubic B-spline (ExCBS) basis functions. The Caputo fractional derivative is applied for temporal discretization, while the ExCBS functions are utilized for spatial discretization. The stability of the method was discussed by the von Neumann method, which shows unconditional stability; and the convergence analysis secure an order of O(h2+\triangle t2-α). We demonstrated the efficiency and simplicity of our method through three numerical experiments and verified its accuracy using the absolute error (L2) and maximum error (L_∞) norms in temporal and spatial dimensions. The results are also graphically represented and show substantial agreement with the approximated and exact solution. We confirmed the effectiveness and accuracy of our approach over the local discontinuous Galerkin finite element and the compact finite difference methods, respectively, from the literature.