Second-order difference equations in diffraction theory

WKB and Turning Point Theory for Second-order Difference Equations

A turning point method for difference equations is developed. This method is coupled with the LG-WKB method via matching to provide approximate solutions to the initial value problem. The techniques developed are used to provide strong asymptotics for Hermite polynomials. Mathematics Subject Classification (2000). Primary 39A10; Secondary 41A60, 65Q05.

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Bounded Solutions to Nonhomogeneous Linear Second-Order Difference Equations

By using some solvability methods and the contraction mapping principle are investigated bounded, as well as periodic solutions to some classes of nonhomogeneous linear second-order difference equations on domains N0, Z \N2 and Z. The case when the coefficients of the equation are constant and the zeros of the characteristic polynomial associated to the corresponding homogeneous equation do not...

On a System of Second-Order Nonlinear Difference Equations

This paper is concerned with dynamics of the solution to the system of two second-order nonlinear difference equations 1 1 1 n n n n x x A x y + − − = + , 1 1 1 n n n n y y A x y + − − = + ,  n = 0,1, , where ( ) 0, A∈ ∞ , ( ) 0, i x− ∈ ∞ , ( ) 0, i y− ∈ ∞ , i = 0, 1. Moreover, the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some num...

On Lie Group Classification of Second{order Ordinary Difference Equations