On singular singularly-perturbed initial value problems
- 1 November 1978
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 8 (1) , 71-81
- https://doi.org/10.1080/00036817808839213
Abstract
Consider the vector initial value problem with for a singular matrix F(t) of constant rank with stable eigenvalues and zero eigenvalues having simple elementary divisors. This paper shows how to determine the unique limiting solution when the reduced problem is solvable and how to obtain a uniform asymptotic expansion for the solution on finite t intervals.Keywords
This publication has 10 references indexed in Scilit:
- Partially Singular Control Problems as Singular Singular-Perturbation Problems 1IFAC Proceedings Volumes, 1978
- Differential equations having rapidly changing solutions: Analytic methods for weakly nonlinear systemsJournal of Differential Equations, 1976
- Differentiation of Pseudoinverses, Separable Nonlinear Least Square Problems and Other TalesPublished by Elsevier ,1976
- Matched Asymptotic Expansion Solutions of Nonlinear Partial Differential Equations with a Small ParameterSIAM Journal on Mathematical Analysis, 1975
- ALTERNATIVE METHODS IN NONLINEAR ANALYSISPublished by Elsevier ,1975
- Singular perturbation problems whose degenerate forms have many solutionsApplicable Analysis, 1972
- Properties of solutions of ordinary differential equations with small parametersCommunications on Pure and Applied Mathematics, 1971
- Singular perturbations on the infinite intervalTransactions of the American Mathematical Society, 1966
- Numerical methods for solving linear least squares problemsNumerische Mathematik, 1965
- The asymptotic behavior of the stable initial manifolds of a system of nonlinear differential equationsTransactions of the American Mathematical Society, 1957