Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A Galerkin solution to a regularized Cauchy singular integro-differential equation

Author: Jay I. Frankel
Journal: Quart. Appl. Math. 53 (1995), 245-258
MSC: Primary 45E05; Secondary 45J05, 65R20
DOI: https://doi.org/10.1090/qam/1330651
MathSciNet review: MR1330651
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Abstract: This paper presents a Galerkin approach for solving a regularized version of the Cauchy singular, linear integro-differential equation

$\displaystyle \frac{{d\Theta }}{{dx}}\left( x \right) - f\left( x \right) = \la... ...^1\frac{{\Theta \left( y \right)}}{{x - y}}dy, \qquad x \in \left( 0, 1 \right)$

, subject to $ \Theta \left( 0 \right) = \Theta \left( 1 \right) = 0$. This equation has appeared in both combined infrared gaseous radiation and molecular conduction, and elastic contact studies. A regularized formulation is produced which suggests the use of an expansion technique where the orthogonal basis functions are chosen as the Chebychev polynomials of the first kind. Accurate results, requiring a minimal computational cost, are formally documented and compared to a purely numerical solution.

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DOI: https://doi.org/10.1090/qam/1330651
Article copyright: © Copyright 1995 American Mathematical Society

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