Approximate solution of MRLW equation in B-spline environment

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.