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This article aims to produce efficient numerical results using the Galerkin approach and quartic B-spline functions for the one-dimensional second-order nonlinear evolution equation. The quartic B-spline functions are used as the shape and weight functions for the Galerkin method. The time derivative and space parameters are discretized by the finite difference and Crank–Nicolson schemes, respectively. A Galerkin approach is investigated by propagating waves at various times and comparisons are made with published papers. The obtained results show that the scheme presented good results and conservations laws are all adequately obeyed.

A Galerkin approach to solitary wave propagation for the second-order nonlinear evolution equation based on quartic B-spline functions