Legendre-Gauss-Radau Collocation Method for Solving Initial Value Problems of First Order Ordinary Differential Equations

Authors:
Zhong-Qing Wang;Ben-Yu Guo
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, P.R. China 200234 and Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institut ...;Department of Mathematics, Shanghai Normal University, Shanghai, P.R. China 200234 and Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science of E-institut ...
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

In this paper, we propose an efficient numerical integration process for initial value problems of first order ordinary differential equations, based on Legendre-Gauss-Radau interpolation, which is easy to be implemented and possesses the spectral accuracy. We also develop a multi-step version of this approach, which can be regarded as a specific implicit Legendre-Gauss-Radau Runge-Kutta method, with the global convergence and the spectral accuracy. Numerical results coincide well with the theoretical analysis and demonstrate the effectiveness of these approaches.