Implicit Runge–Kutta methods based on Lobatto quadrature formula

Abstract

Using W-transformation of Hairre and Wanner, high-order implicit Runge–Kutta (RK) methods based on Lobatto quadrature are studied. Methods constructed and presented include and extend the existing Lobatto III type RK methods. Two to four stages general Lobatto III methods with three parameters α, β, γ are constructed, and a particular one-parameter family Lobatto III C(γ) method is also presented.

Keywords:

• Runge–Kutta method
• Lobatto quadrature
• Symplectic, Stiff accuracy
• A-stability
• L-stability

Acknowledgements

The work of Hongyu Liu was supported by Hong Kong RGC Grants (Project No. CUHK4244/01P and 403403).