On the Asymptotic Expansions for Time-Varying Scalar Differential Equations Possesssing Limiting Differential Equations by Application of the Residue Theorem to their Discretized Counterparts. Preliminary Results

TL;DR

This paper demonstrates that asymptotic expansions for linear time-varying differential equations with limiting behavior can be derived by discretizing the equations and applying residue calculus to their discrete versions.

Contribution

It introduces a novel approach of using residue theorem on discretized equations to obtain asymptotic expansions for time-varying differential equations.

Findings

Asymptotic expansions can be derived via discretization and residue calculation.

The method applies to equations with limiting behavior.

Preliminary results validate the approach.

Abstract

In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then using residues calculation for such discrete- time counterparts