Periodic solutions of non-linear discrete Volterra equations with finite memory

Periodic solutions of discrete Volterra equations

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

On Asymptotically Periodic Solutions of Linear Discrete Volterra Equations

We show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations.

A finite difference method for the smooth solution of linear Volterra integral equations

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

Numerical Solutions of Special Class of Systems of Non-Linear Volterra Integro-Differential Equations by a Simple High Accuracy Method

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...