A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity

doi:10.1007/s10483-018-2299-6

Abstract

Abstract: A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schrödinger (NLS) equations, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.

Key words: vector bundle dynamics, nonuniform hyperbolicity, ergodicity, admissible perturbation, pointwise boundedness, high-order convergence, Galerkin method, generalized nonlinear Schrödinger (NLS) equation, wavelet

2010 MSC Number:

Jiaqun WANG, Xiaojing LIU, Youhe ZHOU. A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 275-290.

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