Asymptotics of Singularly Perturbed Volterra Type Integro-Differential Equation

Abstract

This paper addresses the asymptotic behaviors of a linear Volterra type integro-differential equation. We study a singular Volterra integro equation in the limiting case of a small parameter with proper choices of the unknown functions in the equation. We show the effectiveness of the asymptotic perturbation expansions with an instructive model equation by the methods in superasymptotics. The methods used in this study are also valid to solve some other Volterra type integral equations including linear Volterra integro-differential equations, fractional integro-differential equations, and system of singular Volterra integral equations involving small (or large) parameters.

Keywords

• Volterra integro-differential equations
• Singular perturbation
• asymptotic analysis

References

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