Legendre spectral collocation method for second-order nonlinearordinary/partial differential equations

Lijun Yi; Zhongqing Wang

doi:10.3934/dcdsb.2014.19.299

Article Contents

2014, Volume 19, Issue 1: 299-322. Doi: 10.3934/dcdsb.2014.19.299

This issue Previous Article Dirichlet series for dynamical systems of first-order ordinary differential equations Next Article

Legendre spectral collocation method for second-order nonlinear ordinary/partial differential equations

Lijun Yi^1, and
Zhongqing Wang¹

1.
Department of Mathematics, Shanghai Normal University, Division of Computational Science of E-institute of Shanghai Universities, Shanghai, 200234

Received: August 2012

Revised: September 2013

Published: January 2014

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Abstract

We propose an efficient Legendre-Gauss collocation algorithm for second-order nonlinear ordinary differential equations (ODEs). We also design a Legendre-Gauss-type collocation algorithm for time-dependent second-order nonlinear partial differential equations (PDEs), which can be implemented in a synchronous parallel fashion. Numerical results indicate the high accuracy and effectiveness of the suggested algorithms.

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Mathematics Subject Classification: Primary: 65M70, 41A10, 65L05, 35L20.

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