International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.5, Oct. 2015, Pub. Date: Jun. 24, 2015
Power Series Solutions to Generalized Abel Integral Equations
Pages: 250-254 Views: 1778 Downloads: 5897
[01] Rufina Abdullina, Department of Physics and Mathematics, Sterlitamak Branch of the Bashkir State University, Sterlitamak, Russia.
Even though they have a rather specialized structure, Abel equations form an important class of integral equations in applications. This happens because completely independent problems lead to the solution of such equations. In this paper we consider the generalized Abel integral equation of the first and second kind. Authors have been proposed a new method for constructing solutions of Abel by a power series.
Generalized Abel Integral Equations, Integral Equation, Power Series
[01] R. Gorenflo and S. Vessella, Abel integral Equations: Analysis and Application, Springer-Verlag, Berlin-New York, 1991.
[02] Jerri, A Introduction to Integral Equations with Applications. Wiley, New York, 1999.
[03] Davis, H. T. Introduction to Nonlinear Differential and Integral Equations, 1st ed., Dover Publications, Inc., New York, 1962.
[04] A. V. Manzhirov and A. D. Polyanin, Handbook of Integral Equations: Solution Methods [in Russian], Factorial Press, Moscow, 2000.
[05] Deutsch, M, Beniaminy, I Derivative-free Inversion of AbeVs Integral Equation. Applied Physics Letters 41: pp. 27-28, 1982.
[06] Abel, NH (1826) Auflosung einer Mechanischen Aufgabe. Journal für Reine Angewandte Mathematik 1: pp. 153-157, 1826.
[07] Anderssen, RS Stable Procedures for the Inversion of AbeVs Equation. Journal of the Institute of Mathematics and its Applications 17: pp. 329-342, 1976.
[08] Minnerbo, GN, Levy, ME Inversion of AbeVs Integral Equation by Means of Orthogonal Polynomials. SIAM Journal on Numerical Analysis 6: pp. 598-616, 1969.
[09] J. D. Tamarkin, “On integrable solutions of Abel’s integral equation,” Annals of Mathematics, vol. 31, no. 2, pp. 219–229, 1930.
[10] A.C. Pipkin, A Course on Integral Equations, Springer–Verlag, New York, 1991.
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