In this study, we have modified quintic B-spline base function to use for numerical solution of the Burgers’ equation. For this purpose, the numerical algorithm differential quadrature method and Crank–Nicolson scheme are used for space and time discretization, respectively. To deal with nonlinear terms, they are linearized by using Rubin–Graves technique. To observe the accuracy of the present modification, ten different and important test problems are solved successfully. The present results are compared with earlier single methods and mixed methods to see the efficiency of the present algorithm. All comparisons display that the present approach developed the numerical results according to earlier ones. Numerical simulations are plotted at selected time steps to observe the physical behaviour of the waves in 2D and 3D. The rate of convergence related to space is calculated for different examples and reported with error norms.

在这项研究中，我们修改了五次B样条基函数，以用于Burgers方程的数值解。为此，将数值算法微分求积法和Crank-Nicolson方案分别用于空间和时间离散化。为了处理非线性项，可以使用Rubin–Graves技术将它们线性化。为了观察本修改的准确性，成功解决了十个不同且重要的测试问题。将本结果与较早的单一方法和混合方法进行比较，以了解本算法的效率。所有比较表明，本方法根据较早的方法得出了数值结果。在选定的时间步长处绘制了数值模拟，以观察2D和3D中波的物理行为。