An element-free based solution for nonlinear Schrödinger equations using the ICVMLS-Ritz method

An improved complex variable moving least-squares Ritz (ICVMLS-Ritz) method is proposed for predicting numerical solution of the two-dimensional nonlinear Schrödinger equation. In this element-free solution procedure, the ICVMLS approximation is employed to reduce the number of unknown coefficients in the trial function. It follows by the Ritz procedure to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear Schrödinger equation. The central differencing scheme and Newton's algorithm are adopted to solve the nonlinear equation system. Numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element-free ICVMLS-Ritz method by comparing the computed results with the available analytical solutions.