Singular Equations

Prem K. Kythe and Pratap Puri
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Prem K. Kythe: University of New Orleans
Pratap Puri: University of New Orleans, Department of Mathematics

Chapter 7 in Computational Methods for Linear Integral Equations, 2002, pp 175-212 from Springer

Abstract: Abstract We have so far considered cases where the kernel k(x, s) and the free term f(x) are continuous on [a, b]. The term “singular” has been used in different connotations. Delves and Mohamed (1985) use it to mean any kind of lack of analyticity in an integral equation. However, they distinguish between the following types of singular integral equations: (i) those with a semi-infinite or infinite range; (ii) those with a discontinuous derivative in either the kernel or the free term; and (iii) those with either an infinite or nonexisting derivative of some finite order. Any combination of these situations may also occur in an equation. Singular equations arise in the areas of potential problems,Dirichlet problems,radiative equilibrium,and many others.

Keywords: Iteration Method; Quadrature Rule; Free Term; Singular Kernel; Midpoint Rule (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0101-4_7

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