The extension of the theory of A-methods to RK-methods. (English) Zbl 0682.65041
Numerical treatment of differential equations, Sel. Pap. 4th Int. Semin., NUMDIFF, Halle-Wittenberg/GDR 1987, Teubner-Texte Math. 104, 8-18 (1988).
[For the entire collection see Zbl 0672.00007.]
Any combination of different linear k-step methods generates a composite linear scheme; typical examples are the linear cyclic methods, the block- implicit methods, and also the Runge-Kutta methods (RK-methods). The aim of this paper is to incorporate the theory of RK-methods into the more general theoretical setting of A-methods. The result is a unified approach to a very large class of integration methods.
Any combination of different linear k-step methods generates a composite linear scheme; typical examples are the linear cyclic methods, the block- implicit methods, and also the Runge-Kutta methods (RK-methods). The aim of this paper is to incorporate the theory of RK-methods into the more general theoretical setting of A-methods. The result is a unified approach to a very large class of integration methods.
Reviewer: P.Chocholatý
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
