Helly’s Principle and Its Application to an Infinite-Horizon Optimal Control Problem |
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Authors: | D Bogusz |
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Institution: | (1) Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu, India |
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Abstract: | In this paper, a numerical method is presented to solve singularly-perturbed two-point boundary-value problems for second-order
ordinary differential equations with a discontinuous source term. First, an asymptotic expansion approximation of the solution
of the boundary-value problem is constructed using the basic ideas of the well-known WKB perturbation method. Then, some initial-value
problems and terminal-value problems are constructed such that their solutions are the terms of this asymptotic expansion.
These initial-value problems and terminal-value problems are singularly-perturbed problems and therefore fitted mesh method
(Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples are provided to illustrate
the method. |
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Keywords: | Singular perturbation problems Discontinuous source terms Boundary and interior layers Asymptotic expansion approximations Boundary value problems Initial value problems Initial value methods |
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