Implicit Runge–Kutta methods based on Radau quadrature formula

Abstract

Using W-transformation of Hairer and Wanner, high-order implicit Runge–Kutta methods based on Radau quadrature are studied. Methods constructed and presented include and extend the existing RadauIA, IB, IIA, IIB type RK methods. 2- and 3-stage general Radau RK methods with two parameters (δ, γ) are constructed. The RK methods with five parameters (α, β, γ, δ, τ), which include both Radau and Lobatto type methods, will be discussed at last.

Keywords:

• W-transformation
• symplectic
• algebraically stable
• symmetric
• quadrature formula

2000 AMS Subject Classification :

• 5L05
• 65L06
• 65L20

Acknowledgements

This paper is supported by the National Natural Science Foundation of China (10671047) and of HIT (200713).