Numerical Solution on Neutral Delay Volterra Integro-Differential Equation

Abstract

In this research, the constant type of neutral delay Volterra integro-differential equations (NDVIDEs) are currently being resolved by applying the proposed technique in numerical analysis namely, two-point two off-step point block multistep method (2OBM4). This new technique is being applied in solving NDVIDE, identified as a hybrid block multistep method, developed using Taylor series interpolating polynomials. To complete the algorithm, two alternative numerical approaches are introduced to resolve the integral and differential parts of the problems. Note that the differentiation is approximated by the divided difference formula while the integration is interpolated using composite Simpson’s rule. The proposed method has been analysed thoroughly in terms of its order, consistency, zero stability and convergence. The suitable stability region for 2OBM4 in solving NDVIDE has been constructed and the stability region is built based on the stability polynomial obtained. Consequently, numerical results are presented to demonstrate the effectiveness of the proposed 2OBM4.