The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B‐spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.

中文翻译：

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有限差分法与微分求积法相结合求解修正的等宽波动方程

这项研究的目的是改善修正的等宽波动方程的数值解。为此，已经使用了有限差分法，微分求积法与鲁宾和格雷夫斯线性化技术相结合。修改后的三次B样条基函数用作基函数。通过将两种数值方法和有效的线性化技术相结合，可以获得高精度的数值算法。对于系数的各种值，解决了三个主要的测试问题。为了观察本方法的性能，计算了具有解析解的单孤子问题的误差范数。除了这些错误规范，还报告了三个不变量。结果比较表明，我们的算法产生的结果优于文献中给出的结果。