论文信息 - Convergence results for general linear methods on singular perturbation problems

Convergence results for general linear methods on singular perturbation problems

Many numerical methods used to solve Ordinary Differential Equations, or Differential Algebraic Equations can be written as general linear methods. The B-convergence results for general linear methods are for algebraically stable methods, and therefore useless for nearly A-stable methods. The purpose of this paper is to show convergence for singular perturbation problems for the class of general linear methods without assuming A-stability.

Stefan W. Schneider

[1] Gerhard Wanner,et al. A short proof on nonlinearA-stability , 1976 .

[2] Kevin Burrage,et al. High order algebraically stable Runge-Kutta methods , 1978 .

[3] Michel Crouzeix,et al. On the existence of solutions to the algebraic equations in implicit runge-kutta methods , 1983 .

[4] A. Tikhonov,et al. Linear Differential Equations , 1985 .

[5] J. Butcher. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[6] P. Deuflhard,et al. One-step and extrapolation methods for differential-algebraic systems , 1987 .

[7] Ernst Hairer,et al. Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations , 1988 .

[8] Ernst Hairer,et al. The numerical solution of differential-algebraic systems by Runge-Kutta methods , 1989 .

[9] C. Lubich,et al. On the convergence of multistep methods for nonlinear stiff differential equations , 1992 .

[10] Stefan W. Schneider. Numerical experiments with a multistep Radau method , 1993 .

[11] W. Hundsdorfer. On the error of general linear methods for stiff dissipative differential equations , 1994 .