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Boundary and Initial-Value Methods for Solving Fredholm Equations with Semidegenerate Kernels

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Solution Methods for Integral Equations

Part of the book series: Mathematical Concepts and Methods in Science and Engineering ((MCSENG,volume 18))

Abstract

We develop a new approach to the theory and numerical solution of a class of linear and nonlinear Fredholm equations. These equations, which have semidegenerate kernels, are shown to be equivalent to two-point boundary-value problems for a system of ordinary differential equations. Application of numerical methods for this class of problems allows us to develop a new class of numerical algorithms for the original integral equation. The scope of the paper is primarily theoretical; developing the necessary Fredholm theory and giving comparisons with related methods. For convolution equations, the theory is related to that of boundary-value problems in an appropriate Hilbert space. We believe that the results here have independent interest. In the last section, our methods are extended to certain classes of integrodifferential equations.

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Authors and Affiliations

  1. University of Nevada at Las Vegas, Las Vegas, Nevada, USA

    M. A. Golberg (Professor of Mathematics)

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  1. M. A. Golberg
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Editors and Affiliations

  1. Department of Mathematics, University of Nevada at Las Vegas, Las Vegas, Nevada, USA

    Michael A. Golberg

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Golberg, M.A. (1979). Boundary and Initial-Value Methods for Solving Fredholm Equations with Semidegenerate Kernels. In: Golberg, M.A. (eds) Solution Methods for Integral Equations. Mathematical Concepts and Methods in Science and Engineering, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1466-1_13

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  • DOI: https://doi.org/10.1007/978-1-4757-1466-1_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1468-5

  • Online ISBN: 978-1-4757-1466-1

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