A finite difference scheme for the MRLW and solitary wave interactions

Solitary wave solutions of the MRLW equation using radial basis functions

“…[24] using the Adomian decomposition method, in Ref. [25] using a finite difference scheme, in Ref. [26] using a collocation method with cubic B-splines, in Ref.…”

A numerical technique for solution of the MRLW equation using quartic B-splines

“…The error in invariant C 3 approaches zero during the simulation and maximum absolute errors in C 1 , C 2 remain less than 3.55 Â 10 À3 and 2.0 Â 10 À6 throughout the simulation. In Table 1 the performance of the new method is compared with finite difference method [17] at t = 10. It is observed that errors of the method [17] are considerably larger than those obtained with the present scheme.…”

“…In Table 1 the performance of the new method is compared with finite difference method [17] at t = 10. It is observed that errors of the method [17] are considerably larger than those obtained with the present scheme. Error graph is shown in Fig.…”

“…The conservation properties of the MRLW equation related to mass, momentum and energy are determined by finding the following three invariants [16,22]: We take a = 1, c = 0.03, h = 0.2, Dt = 0.025, l = 1, x 0 = 0, À40 6 x 6 60 to compare our results with [17]. In order to find error norms and the invariants C 1 , C 2 , C 3 at different times, the computations are carried out for times up to t = 10.…”

Numerical solutions of the MRLW equation using moving least square collocation method

“…A …nite di¤erence scheme and Fourier stability analysis in [5], two …nite di¤er-ence approximations for the space dicretization and a multi-time step method for the time discretization for the MRLW equation in [15] and a fully implicit …nite di¤erence method in [19] were presented for the numerical solution of the MRLW equation. Also, the Adomian decomposition method was applied to solve numerically the MRLW equation in [6].…”