Masses from inhomogeneous 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...

Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion

We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean’s caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or stationary front solutions in the case of propagation failure. A general form for these...

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...

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