A Space-Time Fully Decoupled Wavelet Galerkin Method for Solving Multidimensional Nonlinear Schrödinger Equations with Damping

Jiaqun Wang, Youhe Zhou and Xiaojing Liu

Mathematical Problems in Engineering, 2017, vol. 2017, 1-10

Abstract:

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6051597

DOI: 10.1155/2017/6051597

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