In this paper, the numerical solution of the modified regularized long wave equation is obtained using a quartic B-spline approach with the help of Butcher’s fifth-order Runge–Kutta (BFRK) scheme. Here, any kind of transformation or linearization technique is not implemented to tackle the nonlinearity of the equation. The BFRK scheme is applied to solve the systems of first-order ordinary differential equations of time-dependent variables. Three invariants of the motion are evaluated to justify the conservative properties of the recommended scheme. Three examples are illustrated for comparing the present work with the exact solution and the results of others. The stability of the quartic B-spline collocation scheme is found to be unconditionally stable. The main advantage of the proposed scheme is to obtain better approximate solutions by applying the BFRK scheme to solve the systems of first-order ordinary differential equations without transformation or linearization technique.

在本文中，借助于Butcher的五阶Runge-Kutta（BFRK）方案，使用四次B样条方法获得了修正的正则化长波方程的数值解。在这里，没有采用任何形式的变换或线性化技术来解决方程的非线性问题。BFRK方案用于求解时变变量的一阶常微分方程组。对运动的三个不变量进行了评估，以证明推荐方案的保守属性是正确的。举例说明了三个例子，用于比较当前工作与确切的解决方案以及其他解决方案的结果。发现四次B样条搭配方案的稳定性是无条件稳定的。