论文信息 - Error bounds for the solution to the algebraic equations in Runge-Kutta methods

Error bounds for the solution to the algebraic equations in Runge-Kutta methods

In the implementation of implicit Runge-Kutta methods inaccuracies are introduced due to the solution of the implicit equations. It is shown that these errors can be bounded independently of the stiffness of the differential equation considered if a certain condition is satisfied. This condition is also sufficient for the existence and uniqueness of a solution to the algebraic equations. TheBSI-andBS-stability properties of several classes of implicit methods are established.

K. Dekker | K. Dekker

[1] G. Dahlquist. Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .

[2] T. Ström. On Logarithmic Norms , 1975 .

[3] Germund Dahlquist,et al. G-stability is equivalent toA-stability , 1978 .

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

[5] R. Jeltsch,et al. Generalized disks of contractivity for explicit and implicit Runge-Kutta methods , 1979 .

[6] Christoph W. Ueberhuber,et al. The Concept of B-Convergence , 1981 .

[7] On the iteration error in algebraically stable Runge-Kutta methods , 1982 .

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

[9] J. Verwer,et al. Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations , 1984 .

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