A new perspective for the numerical solution of the Modified Equal Width wave equation

Abstract

Finding the approximate solutions to natural systems in the branch of mathematical modelling has become increasingly important and for this end various methods have been proposed. The purpose of the present paper is to obtain and analyze the numerical solutions of Modified Equal Width equation (MEW). This equation is one of those equations used to model nonlinear phenomena which has a significant role in several branches of science such as plasma physics, fluid mechanics, optics and kinetics. Firstly, for the discretization of spatial derivatives, a fifth‐order quintic B‐spline based scheme is directly implemented. Secondly, a forward finite difference formula is applied for the temporal discretization of derivatives with respect to time. Simulation results establish the validity and applicability of the suggested technique for a wide range of nonlinear equations. Then, the newly obtained theoretical consequences are numerically justified by the simulations and test problems. These illustrative test problems are presented verifying the superiority of the newly presented scheme compared to other existing schemes and techniques. The suggested method with symbolic computational software such as, Matlab, is proven as an effective way to obtain the soliton solutions of several nonlinear partial differential equations (PDEs). Finally, the newly obtained results are presented graphically to justify the approximate findings.