In this paper, the discontinuous Legendre wavelet Galerkin method is proposed for the numerical solution of the Burgers–Fisher and generalized Burgers–Fisher equations. This method combines both the discontinuous Galerkin and the Legendre wavelet Galerkin methods. Various properties of Legendre wavelets have been used to find the variational form of the governing equation. This variational form transforms it into a system of ordinary differential equations which will be solved numerically. Some illustrative examples are presented to emphasize the efficiency and reliability of the proposed method.

中文翻译：

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Burgers–Fisher方程和广义Burgers–Fisher方程的数值处理

本文针对Burgers–Fisher方程和广义Burgers–Fisher方程的数值解，提出了不连续的Legendre小波Galerkin方法。该方法结合了不连续的Galerkin方法和Legendre小波Galerkin方法。勒让德（Legendre）小波的各种性质已被用来寻找控制方程的变分形式。这种变分形式将其转换为一个常微分方程组，该方程组将通过数值求解。提出了一些说明性示例，以强调所提出方法的效率和可靠性。