An Initial-Value Theory for Fredholm Integral Equations With Semidegenerate Kernels

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Abstract
The Fredholm integral equation where the kernel is semidegenerate has many applications. The solution of this integral equation may be studied as a function of the upper limit of integration x , while t remains fixed. It is shown that the solution satisfies an initial-value problem. This reformulation is well suited to numerical solution by analog and digital computers. The present paper is one of a series on initial-value methods for Fredholm integral equations. Its considerations are of practical significance since an arbitrary kernel may be approximated by a degenerate kernel to a desired degree of accuracy using standard techniques. Furthermore, the important cases in which the kernel is a Green's function and in which the integral equation is a Volterra equation are both covered by this treatment.

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