This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable components. It is observed that the approximate solution uniformly converges to the exact solution for the aforementioned equation. Also, the convergence of the proposed method is investigated. Numerical examples are given to demonstrate the validity and applicability of the presented method. The numerical results indicate that the proposed method is powerful and effective with a small computational overhead.

翻译：本文在再生核希尔伯特空间中研究了时间分数阶Burgers-Huxley方程的数值解。该方程的解析解以具有易计算分量的收敛级数形式获得。研究表明，近似解对前述方程一致收敛于精确解。同时，本文对所提方法的收敛性进行了探讨。通过数值算例验证了所提方法的有效性与适用性。数值结果表明，该方法计算开销小，且具有强大的求解能力与高效性。