On the Numerical Solution of Nonlinear Volterra–Fredholm Integral Equations by Collocation Methods

Abstract

Particular cases of nonlinear mixed Volterra–Fredholm integral equations of the second kind arise in the mathematical modeling of the spatio-temporal development of an epidemic. This paper is concerned with the numerical solution of general integral equations of this type by continuous-time and discrete-time spline collocation methods. Its focus is on the derivation and analysis of methods of high order of convergence.