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.

Numerical Calculations of the MEW Equation from a New Perspective

“…1 shows the movement of the single solitary wave and the absolute error value. At time t=20, the current error norms are 1.05x10 the table that the newly generated solutions are considerably smaller than those in [14], [17], [18] and [24] and very close to the work [28], and it is also clear that the invariants are very well preserved compared to those given in the table. Implementation 1.3 In the third implementation, the amplitude value is taken as c = 0.75.…”

“…In this case, the displacement of the wave becomes will be shorter. Tablo 4 exhibits the comparison of approximate results with those in previous studies [25] and [28] with time increment ∆t = 0.05. Table 4 shows that the achieved results are quite small.…”

“…The computed analytical values of the invariants for different amplitudes are presented in Table 1. Implementation 1.1 In the first application, the comparison of approximate results with those in previous studies [25]and [28] is presented in Table 2, with time increment ∆t = 0.05 for the largest amplitude value c = 1.0. Fig.…”

“…Implementation 1.4 In the fourth implementation, Tablo 5 submits comparison of the approximate results with works in Refs. [14], [17], [18], [24] and [28] for amplitude value c = 0.75 and time increment ∆t = 0.01. The current error norms are 7.0110 −6 and 4.8510 −6 at time t = 20.…”

“…Saka [27] has implemented collocation algorithms with Quintic B-spline. Additionally, as the work of recent years, Başhan et al [28] have submitted a new perspective for equation. Yagmurlu and Karakaş [29] have proposed Trigonometric cubic B-spline method.…”