Solving Burgers' equation always posses challenges for a small value of viscosity. Here we present a numerical method based on the Haar wavelet collocation method coupled with a nonstandard finite difference (NSFD) scheme for a class of generalized Burgers' equation. In the solution process, the time derivative is discretized by the NSFD scheme and the spatial derivatives are approximated by the Haar wavelets series. The nonlinear terms are linearized with the help of the quasilinearisation process. We illustrate the efficiency of the proposed method by solving several test problems and report their $L_2$-error and $L_{\infty }$-error norms. The derived method is quite easy to implement compared to the other methods. Also, the error analysis of the current method is discussed. It is also observed that for the small number of grid points, the current method produces results that are in great agreement with the analytical solutions.

求解 Burgers 方程总是对小粘度值提出挑战。在这里，我们提出了一种基于 Haar 小波搭配方法和非标准有限差分 (NSFD) 方案的数值方法，用于一类广义 Burgers 方程。在求解过程中，时间导数采用NSFD格式离散，空间导数采用Haar小波级数近似。非线性项在拟线性化过程的帮助下被线性化。我们通过解决几个测试问题来说明所提出方法的效率并报告它们${升}_2$-错误和 ${升}_{\infty }$-错误规范。与其他方法相比，派生方法非常容易实现。此外，还讨论了当前方法的误差分析。还观察到，对于少量网格点，当前方法产生的结果与解析解非常一致。