Logarithmic difference lemma in several complex variables and partial difference equations

Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations ⋆

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented, and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue...

Discrete Orthogonal Polynomials and Difference Equations of Several Variables

The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.

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...

Linearizing Integral Transform and Partial Difference Equations

A linearizing integral transform is proposed which relates solutions of a spectral problem associated with a class of inte-grable partial difference equations to any given solution of the spectral problem. Examples of this class are lattice versions of the isotropic Heisenberg spin chain, the nonlinear SchrSdinger equation and the (complex) sine-Gordon equation. 1. Introduction. Recently a dire...

Matrixtheorems for Partial Differential and Difference Equations