Numerical Solutions Of Mrlw Equation By A Fully Implicit Finite-difference Scheme

Abstract

In the present paper, a fully implicit finite difference method is introduced for the numerical solution of the modified regularized long wave (MRLW) equation. The accuracy of the method is examined by different problems of the MRLW equation. The results and comparisons with analytical and other numerical invariants clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.

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].…”

New scheme for nonlinear Schrödinger equations with variable coefficients

“…The research for deterministic Schrödinger-type equations is well done. There are many investigations for deterministic PDEs, such as exp-function method [8], homotopy perturbation method [23], variational iteration method [22], collocation scheme [16], finite difference method [9] and so on. The numerical analysis for deterministic Schrödinger-type equations, such as symplectic schemes [17] and multi-symplectic schemes [20], pseudospectral method [4], compact method [6], finite volume scheme [7], collocation method [24], and conservative scheme [12,19], can be found in the references therein.…”