A variable stepsize improvement of the trapezoidal rule. (English) Zbl 1138.65053
Summary: An acceleration algorithm for variable stepsize that improves the accuracy of the trapezoidal rule for stiff initial value problems is presented. The estimate of the truncation error is used both to control the stepsize and to make a passive extrapolation to the fourth order. This algorithm is very efficient in the stiff case, because it maintains the stability and does not involve extra calculations.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
