Second order q-difference equations solvable by factorization method

Variational Iteration Method for q-Difference Equations of Second Order

q-Karamata functions and second order q-difference equations

In this paper we introduce and study q-rapidly varying functions on the lattice q0 := {qk : k ∈ N0}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information abo...

Solvable Product-type System of Difference Equations of Second Order

We show that the system of difference equations zn+1 = wa n zb n−1 , wn+1 = zc n wd n−1 , n ∈ N0, where a, b, c, d ∈ Z, and initial values z−1, z0, w−1, w0 ∈ C, is solvable in closed form, and present a method for finding its solutions.

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...

Quasi Exactly Solvable Difference Equations

Several explicit examples of quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/ sin x potential de...