Semilinear integro-differential equations with compact semigroups

Compact finite difference methods for high order integro-differential equations

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...

Optimal Feedback Control of Fractional Semilinear Integro-differential Equations in The Banach Spaces

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

Compact finite difference method for integro-differential equations

In this paper, we give sixth order compact finite difference formula for second order integro-differential equations (IDE) with different boundary conditions, and both of error estimates and numerical experiments confirm our compact finite difference method can get fifth order of accuracy. We also adjust compact finite difference method for first order IDE and a system of IDE and give numerical...

Nonlinear Integro - Differential Equations

On Semilinear Integro-Differential Equations with Nonlocal Conditions in Banach Spaces

and Applied Analysis 3 refer the reader to 11–13 . In order to represent the mild solutions via the variation of constants formula for this case, the notion of so-called resolvent for the corresponding linear equation x′ t A [ x t ∫ t 0 F t − s x s ds ] , t ∈ J 1.8 can be applied. More precisely, an operator-valued function R · : J → L X is called the resolvent of 7 if it satisfies the followin...