Third Order Explicit Multistep Block Method in solving Neutral and Retarded Volterra Delay Integro-Differential Equatio

Advisor:NaolTufa Negaro(PhD) Abstract. In this thesis accurate numerical method for solving neutral Volterra delay integrodifferential equations (NVDIDEs) and retarded Volterra delay integro differential equations (RVDIDEs) is developed. A third-order explicit multistep block method is derived by applying the Taylor series. In addition to achieve more accuracy in the solutions, the step size needs to be very small. The consistency, stability, and convergence of the method are determined. The numerical results obtained have shown that the proposed explicit method is robust and accurate in solving neutral Volterra delay integro-differential equations and retarded Volterra delay integro differential equations compared with other numerical method. Lastly, to validate the theoretical predictions three numerical examples are taken and analyzed for different steps sizes and demonstrated by table and graphs. Keywords: Multistep block:Volterra delay integro differential equation: Neutral Volterra delay integro-differential equations: Retarded Volterra delay integro differential equations: