A space-time fully decoupled wavelet Galerkin method for solving multidimensional nonlinear Schrödinger equations with damping
type: Item
instance of: scholarly article
title: A space-time fully decoupled wavelet Galerkin method for solving multidimensional nonlinear Schrödinger equations with damping
zbMATH Open document ID: 1427.65266
DOI: 10.1155/2017/6051597
author: Jiaqun Wang
author: Xiaojing Liu
author: Youhe Zhou
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: On the basis of sampling approximation for a function defined on a bounded interval by combining Coiflet-type wavelet expansion and technique of boundary extension, a space-time fully decoupled formulation is proposed to solve multidimensional Schrödinger equations with generalized nonlinearities and damping. By applying a wavelet Galerkin approach for spatial discretization, nonlinear Schrödinger equations are first transformed into a system of ordinary differential equations, in which all matrices are completely independent of time and never need to be recalculated in the time integration. Then, the classical fourth-order explicit Runge-Kutta method is used to solve the resulting semidiscretization system. By studying several widely considered test problems, results demonstrate that when a relatively fine mesh is adopted, the present wavelet algorithm has a much better computational accuracy and efficiency than many existing numerical methods, due to its higher order of convergence in space which can go up to 6.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 6972287
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/6051597
OpenAlex ID: W2768393767
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description: scientific article; zbMATH DE number 6972287