Local Estimation of the Global Discretization Error
- 1 September 1971
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 8 (3) , 512-523
- https://doi.org/10.1137/0708049
Abstract
The lowest order term of the global discretization error of the numerical solution to a system of ordinary differential equations satisfies a well-known differential equation. It is observed that the integration of this differential equation and thus the estimation of the discretization error becomes almost trivial if it is an exact differential equation. It is shown that there exist both RK-methods and multistep methods, the error equation of which is exact.Keywords
This publication has 5 references indexed in Scilit:
- Cyclic Composite Multistep Predictor-Corrector MethodsSIAM Journal on Numerical Analysis, 1971
- The effective order of Runge-Kutta methodsLecture Notes in Mathematics, 1969
- The numerical integration of ordinary differential equationsMathematics of Computation, 1967
- Asymptotic expansions for the error of discretization algorithms for non-linear functional equationsNumerische Mathematik, 1965
- Coefficients for the study of Runge-Kutta integration processesJournal of the Australian Mathematical Society, 1963