Error analysis of piecewise collocation method for delay integro-differential–algebraic equations

Abstract

Piecewise collocation method for integro-differential–algebraic equations (IDAEs) with non-vanishing delay is applied. The theory needed to understand the numerical approach and analyze the numerical treatment by collocation methods is developed. Based on the structure of solutions of delay IDAEs and identification of initial discontinuity points, numerical analysis and properties of the convergence are investigated. Here, collocation method which depends on the numerical solution in a fixed number of previous time steps is described by the constructive technique and dividing the definition domain into several subintervals according to the initial discontinuous points associated with the delay function. Finally, the numerical experiments are given to demonstrate the conclusions.