High-Order Coefficients of Second-Order ODEs in Relation to Pre-Factors for Complex Parameter

Authors : Fatih SAY

Pages : 52-56

Doi:10.33401/fujma.725913

View : 17 | Download : 13

Publication Date : 2020-06-10

Article Type : Research Paper

Abstract :In this study, we asymptotically reconsider the relations between the pre-factors of a general inhomogeneous second-order ordinary differential equation and the high-order coefficients of its asymptotic power series for complex values of the asymptotic parameter $ \epsilon_{1} $. The study provides a general formula for its generic high-order coefficients with the associated pre-factors for complex $ \epsilon_{1} $ based on the use of a well-known factorial divided by a power approach.
Keywords : Asymptotic expansions, Approximation, Asymptotic beyond all orders, Perturbation, Series solutions