论文信息 - Error of Partitioned Runge-Kutta Methods for Multiple Stiff Singular Perturbation Problems

Error of Partitioned Runge-Kutta Methods for Multiple Stiff Singular Perturbation Problems

Abstract The main purpose of this paper is to deal with error behaviour of partitioned Runge-Kutta methods for one-parameter multiple stiff singular perturbation problems whose stiffness is caused by a small parameter ε and some other factors and to present some quantitative convergence results.

Aiguo Xiao | Shoufu Li | A. Xiao | Shoufu Li

[1] K. Burrage,et al. Stability Criteria for Implicit Runge–Kutta Methods , 1979 .

[2] L. Segel,et al. Introduction to Singular Perturbations. By R. E. O'MALLEY, JR. Academic Press, 1974. $ 16.50. , 1975, Journal of Fluid Mechanics.

[3] Christoph W. Ueberhuber,et al. Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems , 1985 .

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

[5] Rüdiger Weiner,et al. Order results for Rosenbrock type methods on classes of stiff equations , 1991 .

[6] Stefan W. Schneider. Convergence results for general linear methods on singular perturbation problems , 1993 .

[7] Christoph W. Ueberhuber,et al. Stability Properties of Implicit Runge–Kutta Methods , 1985 .

[8] P. Kokotovic. Applications of Singular Perturbation Techniques to Control Problems , 1984 .