Numerical method in solving neutral and retarded Volterra delay integro-differential equations

Abstract

The aim of this research is to produce accurate numerical results in solving neutral Volterra delay integro-differential equations (NVDIDE) and retarded Volterra delay integro-differential equations (RVDIDE) of constant type. A third-order explicit multistep block method is derived by applying the Taylor series. The consistency, zero stability, and convergence of the method are determined. The problems are solved by approximating two points simultaneously with constant step size. The delay arguments are approximated using previously calculated values while the integration part is approximated using the quadrature rule. The numerical results obtained have shown that the proposed explicit method is comparable with the other methods and is assumed to be reliable in solving NVDIDE and RVDIDE of constant type.