Numerical solution of the time fractional nonlinear burgers equation using the quintic B-Spline method

Nashmi, Fahad Kamil; Taha, Bushra Aziz

doi:10.22124/jmm.2025.31069.2784

Numerical solution of the time fractional nonlinear burgers equation using the quintic B-Spline method

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq.

² Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq

10.22124/jmm.2025.31069.2784

Abstract

This paper introduced a novel approach for resolving fractional partial differential equations.
The time fractional nonlinear Burgers equation of order k was solved to illustrate the efficacy
of the technique, where k in (0;1]. The quintic B-spline method facilitated spatial partitioning, while the finite difference method addressed the fractional Caputo derivative, which simulates anomalous diffusion processes influenced by memory effects. The proposed methods stability is demonstrated utilizing the von Neumann technique; it has been shown to be unconditionally stable. Additionally, a convergence study is shown, demonstrating that the approach exhibits uniform convergence of (gh4 +s(Dh2)). We validated the methods correctness through numerical tests by comparing it with the exact solution and alternative numerical methods. Based on L2 and L¥ error norms, the quintic B-spline approach exhibits improved convergence rates and reduced computing costs.

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