The Numerical Solution of Volterra Integro-Differential Equations with State-Dependent Delay

Abstract

This paper presents the piecewise collocation method for a class of functional integro-differential equations with state-dependent delays. A numerical analysis is applied to solve the delay integro-differential equation and detect the points that have discontinuity in the derivatives of the solution of the problem and insert them into the mesh to guarantee the required accuracy. The convergence analysis of the method is investigated and a numerical experiment is presented for clarifying the robustness of the method.