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Hilbert空间中研究了时间分数阶Burgers-Huxley方程的数值解。该方程的解析解以易于计算的收敛级数形式给出。研究表明，上述方程的近似解一致收敛于精确解。此外，对该方法的收敛性进行了分析。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，该方法具有计算量小、高效可靠的优点。