Boundary and initial-value methods for solving Fredholm equations with semidegenerate kernels |
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Authors: | M A Golberg |
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Institution: | (1) University of Nevada at Las Vegas, Las Vegas, Nevada |
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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. |
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Keywords: | Integral equations Fredholm equations boundary-value problem numerical solution Cauchy problem |
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