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1986•SIAM Journal on Mathematical AnalysisRequires access

Asymptotic Analysis of Singular Singularly Perturbed Boundary Value Problems

Christian Schmeiser, Richard Weiß

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Abstract

Singularly perturbed systems ordinary differential equations for which the reduced system has a manifold of solutions are called singular singularly perturbed. Boundary value problems for a general class of such systems are examined. Conditions are derived which ensure the existence of a locally unique solution, which can be approximated by an asymptotic expansion. The main tool for our analysis is the theory of boundary value problems on long intervals.

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What this paper is about

Singularly perturbed systems ordinary differential equations for which the reduced system has a manifold of solutions are called singular singularly perturbed. Boundary value problems for a general class of such systems are examined. Conditions are derived which ensure the existence of a locally unique solution, which can be approximated by an asymptotic expansion. The main tool for our analysis is the theory of boundary value problems on long intervals.

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Available abstract

Singularly perturbed systems ordinary differential equations for which the reduced system has a manifold of solutions are called singular singularly perturbed. Boundary value problems for a general class of such systems are examined. Conditions are derived which ensure the existence of a locally unique solution, which can be approximated by an asymptotic expansion. The main tool for our analysis is the theory of boundary value problems on long intervals.

Key concepts: Method of matched asymptotic expansions, Mathematics, Singular perturbation, Mathematical analysis, Boundary value problem, Ordinary differential equation, Asymptotic analysis, Asymptotic expansion

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