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Singular Equations

In: Computational Methods for Linear Integral Equations

Author

Listed:
  • Prem K. Kythe

    (University of New Orleans)

  • Pratap Puri

    (University of New Orleans, Department of Mathematics)

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.

Suggested Citation

  • Prem K. Kythe & Pratap Puri, 2002. "Singular Equations," Springer Books, in: Computational Methods for Linear Integral Equations, chapter 7, pages 175-212, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0101-4_7
    DOI: 10.1007/978-1-4612-0101-4_7
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