Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

Alternating Implicit Block FDTD Method For Scalar Wave Equation

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximu...

A spatial sixth-order alternating direction implicit method for two-dimensional cubic nonlinear Schrödinger equations

Based on the combined compact difference scheme, an alternating direction implicit method is proposed for solving two-dimensional cubic nonlinear Schrödinger equations. The proposed method is sixth-order accurate in space and second-order accurate in time. The linear Fourier analysis method is exploited to study the stability of the proposed method. The efficiency and accuracy of the proposed m...

Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations

In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and three dimensions. The proposed method is based on a time-splitting method that decomposes the original problem into two parts, a linear equation and a nonlinear equation. The linear equation in one dimension is approximatedwith the Chebyshev pseudo-spectral collocationmethod in space variable and the Crank–...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method