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

  • M. A. Golberg
Part of the Mathematical Concepts and Methods in Science and Engineering book series (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.

Keywords

Integral Equation Fredholm Integral Equation Integrodifferential Equation Volterra Equation Adjoint Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

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

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