Linear quasi-parabolic integro-differential equations and their control appear in many scientific problems and engineering applications such as biology mechanics, nuclear reaction dynamics, heat conduction in materials with memory, and visco-elasticity, etc.. The existence and uniqueness of the solution of the linear quasi-parabolic integro-differential equations have been studied by Wheeler M....

The present paper deals with the numerical solution for a general form of system nonlinear Volterra delay integro-differential equations (VDIDEs). main purpose this work is to provide a...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and HalfSweep Gauss-Seidel (HS...

We derive error estimates for approximate (viscosity) solutions of Bellman equations associated to controlled jump-diffusion processes, which are fully nonlinear integro-partial differential equations. Two main results are obtained: (i) error bounds for a class of monotone approximation schemes, which includes finite difference schemes, and (ii) bounds on the error induced when the original Lév...