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NUMERICAL ANALYSIS OF LEGENDRE-GAUSS-RADAU AND LEGENDRE-GAUSS COLLOCATION METHODS
NUMERICAL ANALYSIS OF LEGENDRE-GAUSS-RADAU AND LEGENDRE-GAUSS COLLOCATION METHODS
Journal of applied mathematics & informatics. 2015. Sep, 33(5_6): 657-670
  • Received : February 05, 2015
  • Published : September 30, 2015
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CHEN DAOYONG
TIAN HONGJIONG

Abstract
In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.
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