University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 A highly accurate numerical technique for solving variable-order fractional Burgers-Huxley equation 721 733 19706 10.22034/cmde.2025.63198.2820 EN Mojtaba Hajipour Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran. Yashar Lakpour Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran. Journal Article 2024 08 29 In this article, we present a highly accurate technique for the numerical solution of the variable-order time-fractional Burgers-Huxley equation. The original equation is first discretized in the temporal and spatial directions. The third-order weighted-shifted Gr\"unwald-Letnikov and the fourth-order compact finite difference methods are used. We then formulate a nonlinear system of algebraic equations using the fully discretized version of the problem. The derived nonlinear system is solved by utilizing an iterative algorithm. The analysis of solvability, stability, and convergence of the method is also addressed. The method achieves a convergence rate of four in the spatial direction and three in the temporal direction. Moreover, it is a low-cost computational method and easy to implement. Finally, various illustrative examples are solved to verify the accuracy of the proposed method. https://cmde.tabrizu.ac.ir/article_19706_5154d81471d30519caafa89702ff2fa5.pdf