Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear p...

The spatial discretization of initial-boundary-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multistep formulas, using special factorization (or splitting) techniques in the iterative solut...

Nonlinear integral inequalities of Gronwall-Bihari type for piecewise continuous functions are solved. Inequalities for functions with delay as well as functions without delays are considered. Some of the obtained results are applied in the deriving of estimates for the solutions of impulsive integral, impulsive integro-differential and impulsive differential-difference equations.

This paper studies the problems of local exact controllability of nonlinear and global exact null controllability of linear parabolic integro-differential equations respectively with mixed and Neumann boundary data with distributed controls acting on a subdomain ω of Ω ⊂ R. The proof of the linear problem relies on a Carleman-type estimate and observability inequality for the adjoint equations ...

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions integro-sum inequalities; impulse integral inequalities . Some applications of the results are included: conditions of boundedness uniformly , stability by Lyapunov uniformly , practical stability by Chetaev uniformly for the solutions of impulsive differential and integrodifferential ...

The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooper...