Block implicit hybrid one-step methods. (English) Zbl 0711.65051
A class of block implicit hybrid methods is investigated. The implicit equations involve the solution at \(k\) grid points and \(k\) off step points and each block is independent of the previous block. It is shown that a unique method exists of order \(2k+2\) and that these methods are \(A\)-stable for \(k=1,2,...,5\). The coefficients of these 5 methods are given and some numerical results are reported for the \(k=2\), order 6 method.
Reviewer: G.Hall
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
