Finite difference method combined with differential quadrature method for numerical computation of the modified equal width wave equation

Abstract

The aim of this study is to improve the numerical solution of the modified equal width wave equation. For this purpose, finite difference method combined with differential quadrature method with Rubin and Graves linearizing technique has been used. Modified cubic B-spline base functions are used as base function. By the combination of two numerical methods and effective linearizing technique high accurate numerical algorithm is obtained. Three main test problems are solved for various values of the coefficients. To observe the performance of the present method, the error norms of the single soliton problem which has analytical solution are calculated. Besides these error norms, three invariants are reported. Comparison of the results displays that our algorithm produces superior results than those given in the literature.

Numerical Calculations of the MEW Equation from a New Perspective

“…The newly produced solutions are compared with the existing applications in the literature and their behavior is depicted in graphs. As a result of those comparisons, it can be clearly seen that the proposed algorithm shows the best performance according all previous studies [11,12], [14][15][16][17][18][19], [21][22][23][24][25][26][27][28][29], including those in recent years in the literature. These excellent results are new in terms of accuracy, reliability and cost compared to the results of other applications.…”

“…Implementation 1.9 In the ninth implementation, to do the comparison with other studies [15], time increment ∆t = 0.1 is utilized. Comparison of the gained results are done with three different variants of the finite difference method and are submitted at [11,12], [14], [16][17][18][19], [21], [22][23][24][25], [28] and [29] in the literature with the new application for time increment ∆t = 0.05 and amplitude c = 0.25. The current error norms are 2.66x10 −7 and 3.19x10 −7 at t = 20.…”

“…Dereli [22] has researched by utilizing meshless method based on collocation with the well-known radial basis functions. Başhan et al [23] have worked the finite difference method combined with differential quadrature method. Karakoç et al [24] have used different linearization techniques with the help of cubic B-spline collocation FEM.…”

Single Solitary Wave and Wave Generation Solutions of the Regularised Long Wave (RLW) Equation

“…Bellman et al [39] suggested DQM for approximating of the differential equations. In the past decades, many different base functions have been used for numerical solutions of the differential equations [40][41][42][43][44][45][46][47].…”