In this work, we focus on the modified high-order Haar wavelet numerical method, which introduces the third-order Runge–Kutta method in the time layer to improve the original numerical format. We apply the above scheme to two types of strong nonlinear solitary wave differential equations named as the generalized Burgers–Fisher equation and the generalized Burgers–Huxley equation. Numerical experiments verify the correctness of the scheme, which improves the speed of convergence while ensuring stability. We also compare the CPU time, and conclude that our scheme has high efficiency. Compared with the traditional wavelets method, the numerical results reflect the superiority of our format.

中文翻译：

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广义 Burgers-Fisher 方程和广义 Burgers-Huxley 方程中采用 Runge-Kutta 方法的修正高阶 Haar 小波格式

在这项工作中，我们专注于改进的高阶 Haar 小波数值方法，该方法在时间层引入了三阶 Runge-Kutta 方法来改进原始数值格式。我们将上述方案应用于两类强非线性孤立波微分方程，称为广义 Burgers-Fisher 方程和广义 Burgers-Huxley 方程。数值实验验证了方案的正确性，在保证稳定性的同时提高了收敛速度。我们还比较了 CPU 时间，得出我们的方案效率高的结论。与传统的小波方法相比，数值结果体现了我们格式的优越性。