A nonlinear optimization approach to the construction of general linear methods of high order. (English) Zbl 0879.65051
The construction of diagonally implicit multistage integration methods of order and stage order \(p=q=7\) and \(p=q=8\) is presented. Both type 1 (explicit) and type 2 (implicit) methods are obtained. The construction is based on the variable-model trust-region least-squares algorithms.
Reviewer: T.E.Simos (Xanthi)
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
Keywords:
general linear methods; A-stability; L-stability; least-squares minimization; diagonally implicit multistage integration methodsReferences:
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