Singular perturbation analysis of a certain volterra integral equation |
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Authors: | W E Olmstead Richard A Handelsman |
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Institution: | 1. Technological Institute, Northwestern University, Evanston, Illinois, USA 2. Dept. of Mathematics, University of Illinois at Chicago Circle, Chicago, Illinois, USA
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Abstract: | An investigation is made of the asymptotic behavior of the solutionu(t;ε) to the Volterra integral equation $$\varepsilon u(t;\varepsilon ) = \pi ^{ - \tfrac{1}{2}} \int\limits_0^t {(t - s)^{ - \tfrac{1}{2}} f(s) - u^n (s;\varepsilon )]} ds, t \geqslant 0, n \geqslant 1$$ , in the limit as ε→0. This investigation involves a singular perturbation analysis. For the linear problem (n=1) an infinite, uniformly valid asymptotic expansion ofu(t;ε) is obtained. For the nonlinear problem (n≥2), the leading two terms of a uniformly valid expansion are found |
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