Journal of Scientific Computing

, Volume 52, Issue 1, pp 226–255 | Cite as

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

  • Zhong-qing Wang
  • Ben-yu Guo


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.


Legendre-Gauss-Radau collocation method Initial value problems of ordinary differential equations Global convergence Spectral accuracy 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Normal UniversityShanghaiP.R. China
  2. 2.Scientific Computing Key Laboratory of Shanghai UniversitiesDivision of Computational Science of E-institute of Shanghai UniversitiesShanghaiP.R. China

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