Sequential step control for integration of two-point boundary value problems. (English) Zbl 0619.65070
Numerical analysis, Proc. 4th IIMAS Workshop, Guanajuato/Mex. 1984, Lect. Notes Math. 1230, 221-234 (1986).
[For the entire collection see Zbl 0598.00014.]
This paper is concerned with the step size control for the basic discretization. A special form of error indicator is described, which should permit the use of step sizes appropriate to the particular solution. Such an indicator is obtained as the difference between a special explicit predicted value and a matched implicit corrected value. The linked corrector formulae must be solved by a modified Newton iteration to obtain the derived stability properties. Also, the feasibility of finding smooth solutions with appropriate step sizes, by the use of suitable sets of predictor-corrector formulae is given.
This paper is concerned with the step size control for the basic discretization. A special form of error indicator is described, which should permit the use of step sizes appropriate to the particular solution. Such an indicator is obtained as the difference between a special explicit predicted value and a matched implicit corrected value. The linked corrector formulae must be solved by a modified Newton iteration to obtain the derived stability properties. Also, the feasibility of finding smooth solutions with appropriate step sizes, by the use of suitable sets of predictor-corrector formulae is given.
Reviewer: P.Chocholatý
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
