时间分数阶Burgers-Huxley方程描述反应机制与扩散输运相互作用的新解析解
New analytical solution for time fractional Burgers-Huxley equation describing the interaction between reaction mechanisms and diffusion transport
AI总结：
本文在再生核希尔伯特空间中求解时间分数阶Burgers-Huxley方程，提出以收敛级数形式获得解析解，并验证了近似解的一致收敛性，数值算例表明方法高效且计算开销小。
摘要：
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。该方程的解析解以易于计算的收敛级数形式获得。观察到上述方程的近似解一致收敛于精确解。此外，还研究了所提出方法的收敛性。给出了数值算例以验证所提方法的有效性和适用性。数值结果表明，所提方法在计算开销较小的情况下具有强大且有效的性能。
英文摘要：
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.
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