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Boundary and initial-value methods for solving Fredholm equations with semidegenerate kernels

  • M. A. Golberg
Contributed Papers

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. Applications 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.

Key Words

Integral equations Fredholm equations boundary-value problem numerical solution Cauchy problem 

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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • M. A. Golberg
    • 1
  1. 1.University of Nevada at Las VegasLas Vegas

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