Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, a system of conjugate elliptic equations with a small parameter at the highest derivatives is considered in a rectangle with two sides parallel to the characteristics of the limiting equations.
Abstract: A system of two conjugate elliptic equations with a small parameter at the highest derivatives is considered in a rectangle with two sides parallel to the characteristics of the limiting equations.The method of matched asymptotic expansions is used for the construction of uniform asymptotic series for solutions of this system up to an arbitrary power of the small parameter.
2 citations
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01 May 19762 citations
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01 Jan 2010TL;DR: In this paper, the authors studied the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small and derived asymptotic expansions of the free boundary for both small time and large time.
Abstract: This paper studies the borrower’s optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner’s point of view.
2 citations
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04 Dec 1975-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, a rigorous justification is given of work done by Eagles (1969), in which he applied the method of matched asymptotic expansions to the Orr-Sommerfeld equation to obtain formal uniform Asymptotics to a certain pair of solutions.
Abstract: A rigorous justification is given of work done by Eagles (1969), in which he applied the method of matched asymptotic expansions to the Orr-Sommerfeld equation to obtain formal uniform asymptotic approximations to a certain pair of solutions. (Somewhat more polished formal expansions of the same general kind were subsequently obtained by Reid (1972).) First, a study is made of the asymptotic properties of solutions of a certain differential equation which admits the Orr—Sommerfeld equation as a special case. Previous work on this differential equation by Lin & Rabenstein ( i960, 1969) is extended to develop a theory suited to our main purpose: to prove the validity of Eagles’s approximations. It is then shown how this theory can be used to prove the existence of actual solutions of the Orr—Sommerfeld equation approximated by these formal expansions. In addition, it is verified that these solutions have the properties assumed by Eagles (1969).
2 citations