Two-Point Hybrid Multistep Block Method for Solving First-Order Initial Value Problems of Volterra Integro-Differential Equation with Neutral Delay

Abstract

A generalized two-point hybrid multistep block method is proposed for solving Volterra integro-differential equations with neutral delay (NVDIDEs). Initial value problems (IVPs) for NVDIDEs are estimated synchronously at two points, along with an off-grid point forming a hybrid block scheme. Detailed strategies for solving the integral and differential parts are addressed. Convergence and stability analyses of the developed method are analyzed with the stability region derived from the stability polynomial. Numerical results are provided to evaluate the performance of the proposed method in comparison to existing non-block methods. The results are concluded to be comparable with the existing methods and reliable to solve NVDIDE.