QUALITATIVE THEORY OF PARTIAL DIFFERENCE EQUATIONS (V): STURMIAN THEOREMS FOR A CLASS OF PARTIAL DIFFERENCE EQUATIONS

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

Some oscillatory properties for a class of partial difference equations

In this paper we study the oscillatory property of solutions for a class of partial difference equation with constant coefficients. In order to study the oscillation results, we find the regions of nonexistence of positive roots of its characteristic equation which is equivalent to the oscillation results. We derive some necessary and sufficient conditions by means of the envelope theory. c ©20...

Matrixtheorems for Partial Differential and Difference Equations

Tensor Product Analysis of Partial Difference Equations

1. Introduction. This note presents a few of the results which we have obtained by applying a classical and fundamental idea to the analysis of certain partial difference equations. The idea is that certain multidimensional problems can be solved by solving a few one-dimensional problems—it is the basis of the classical method of separation of variables of mathematical physics. In the case of p...

Nonlinear Elliptic Partial Difference Equations on Graphs

This article initiates the study of nonlinear elliptic partial difference equations (PdE) on graphs. We seek solutions u : V → R to the semilinear elliptic difference equation −Lu + f(u) = 0 on a graph G = (V,E), where L is the (negative) Laplacian on the graph G. We extend techniques used to prove existence theorems and derive numerical algorithms for the partial differential equation (PDE) ∆u...