On one class of numerical methods for solving stiff systems of differential equations
Tóm tắt
The paper is concerned with a modification of a Cowell-type method: at each step the solution is evaluated at several points and only some first of these values are retained. Stability of these methods is examined. In particular, among the methods of this group we single out one method that has the fourth order of accuracy and is stable for stiff systems with any choice of integration step.
Tài liệu tham khảo
V. I. Krylov, V. V. Bobkov, and P. I. Monastyrnyi, Computational Methods in Higher Mathematics, Vol. 2 (Vysheishaya Shkola, Minsk, 1975) [in Russian].
G. Hall and J. M. Watt, Modern Numerical Methods for Ordinary Differential Equations (Clarendon Press, Oxford, 1976; Mir, Moscow, 1979).
V. I. Krylov, V. V. Bobkov, and P. I. Monastyrnyi, Foundations of the Theory of Numerical Methods: Differential Equations (Nauka i Tekhnika, Minsk, 1982) [in Russian].
A. N. Krylov, Lectures on Approximate Computations (GITTL, Moscow-Leningrad, 1950) [in Russian].