Plancherel–Rotach asymptotics of second-order difference equations with linear coefficients

Plancherel-Rotach asymptotics of second-order difference equations with linear coefficients

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...

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Second-order Linear Systems with Summable Coefficients*

Sturm and his successors! have examined in detail properties of the zeros of solutions of linear differential systems similar to (1), (3) below, and of linear combinations similar to (2). They have commonly employed the continuity and existence of derivatives of the coefficients. Under more lenient assumptions, the writer will obtain sufficient conditions that the zeros of the linear combinatio...

TWOFOLD q-GEVREY ASYMPTOTICS FOR LINEAR SINGULARLY PERTURBED q-DIFFERENCE-DIFFERENTIAL EQUATIONS WITH POLYNOMIAL COEFFICIENTS

We construct analytic and formal solutions for a family of q-difference-differential problems, under the action of a perturbation parameter. This work is a continuation of the study [10] focusing on a singularly perturbed q-difference-differential problem for which a phenomenon of multilevel q-Gevrey asymptotics has been observed, owing to the fact that the main equation is factorized as a prod...