The Numerical Solution of Boundary Value Problems for Stiff Differential Equations
- 1 January 1977
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 31 (137) , 66-93
- https://doi.org/10.2307/2005781
Abstract
The numerical solution of boundary value problems for certain stiff ordinary differential equations is studied. The methods developed use singular perturbation theory to construct approximate numerical solutions which are valid asymptotically; hence, they have the desirable feature of becoming more accurate as the equations become stiffer. Several numerical examples are presented which demonstrate the effectiveness of these methods.Keywords
This publication has 33 references indexed in Scilit:
- An Algorithm, Based on Singular Perturbation Theory, for Ill-Conditioned Minimization ProblemsSIAM Journal on Numerical Analysis, 1977
- Difference approximations for singular perturbations of systems of ordinary differential equationsNumerische Mathematik, 1974
- An effective numerical integration method for typical stiff systemsAIChE Journal, 1974
- Transition layers in singular perturbation problemsJournal of Differential Equations, 1974
- Semilinear elliptic boundary value problems with small parametersArchive for Rational Mechanics and Analysis, 1973
- Numerical Initial Value Problems in Ordinary Differential EquationsMathematics of Computation, 1973
- An Example of Ill-Conditioning in the Numerical Solution of Singular Perturbation ProblemsMathematics of Computation, 1971
- The Numerical Solution of Singular Perturbations of Boundary Value ProblemsSIAM Journal on Numerical Analysis, 1970
- The Numerical Solution of Linear Boundary Value ProblemsSIAM Review, 1966
- Numerical treatment of ordinary differential equations by extrapolation methodsNumerische Mathematik, 1966