Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
More filters
••
TL;DR: In this article, the authors derived uniform asymptotic expansions of solutions to the fourth-order differential equation where x is a real variable and λ is a large positive parameter.
Abstract: In this paper, we derive uniform asymptotic expansions of solutions to the fourth order differential equation
where x is a real variable and λ is a large positive parameter. The solutions of this differential equation can be expressed in the form of contour integrals, and uniform asymptotic expansions are derived by using the cubic transformation introduced by Chester, Friedman, and Ursell in 1957 and the integration-by-part technique suggested by Bleistein in 1966. There are two advantages to this approach: (i) the coefficients in the expansion are defined recursively, and (ii) the remainder is given explicitly. Moreover, by using a recent method of Olde Daalhuis and Temme, we extend the validity of the uniform asymptotic expansions to include all real values of x.
3 citations
••
3 citations
••
TL;DR: In this paper, it was shown that an infinity of different uniform asymptotic expansions can be constructed for each type of development for the Kouyoumjian and Pathak formulation on a rigorous basis.
Abstract: By exhibiting the development of the Pauli-Clemmow method in a new manner, it is shown that the two uniform asymptotic expansions commonly used are different. Next it is shown that an infinity of different uniform asymptotic expansions can be constructed for each type of development. This allows us to set the Kouyoumjian and Pathak formulation on a rigorous basis. © 1993 John Wiley & sons, Inc.
3 citations