Improved asymptotic expansion for the exponential integral with positive argument

On the asymptotic expansion of certain plane singular integral operators

*Correspondence: [email protected] Chair of Differential Equations, Belgorod National Research University, Studencheskaya 14/1, Belgorod, 308007, Russia Abstract We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representation...

Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument

Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales.

We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral, [Formula: see text] as [Formula: see text], using the distributional approach of McClure & Wong. We find that, for half-integer orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the ...

Global Asymptotic Behavior of Positive Solutions for Exponential Form Difference Equations with Three Parameters∗

In this paper, we study a class of second order difference equations with three paremeters. With positive initial values, the asymptotic behavior of positive solutions are investigated.

Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...