On the asymptotic solution of a nonlinear Volterra integral equation

Abstract

A technique based on the analytic continuation and study of the pole diagram of the Mellin transform has been described for obtaining asymptotic solution of nonlinear Volterra type integral equations for small and large values of the argument. Solutions to a number of problems in nonlinear heat conduction and boundary-layer heat transfer have been presented. By comparison of the results obtained by the present method with solutions obtained earlier by numerical and iterative procedures, it is shown that the technique provides simple and quite accurate solution to problems which were hitherto tackled by numerical methods.