A variational principle for adaptive approximation of ordinary differential equations. (English) Zbl 1053.65059
The authors present an estimate for the global error in the numerical solution of an ordinary differential equation as a weighted sum of the local errors where the weights are found by solving the adjoint of the linearized equation. They also show that the estimate coincides to lowest order with several alternative estimates.
Reviewer: J. D. P. Donnelly (Oxford)
MSC:
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
