Solution of Linear Integral Equations Using Padé Approximants

It is shown that the exact solution of a nonhomogeneous linear integral equation with a kernel K of rank n is given by forming the Padé approximant P(n, n) from the first 2n terms of the perturbation series solution. It follows that for a compact kernel K, the solution is lim n→∞ P(n, n); this gives...

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Bibliographic Details
Published in:Journal of mathematical physics 1963-12, Vol.4 (12), p.1506-1510
Main Author: Chisholm, J. S. R.
Format: Article
Language:English
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Summary:It is shown that the exact solution of a nonhomogeneous linear integral equation with a kernel K of rank n is given by forming the Padé approximant P(n, n) from the first 2n terms of the perturbation series solution. It follows that for a compact kernel K, the solution is lim n→∞ P(n, n); this gives meaning to a large class of perturbation series when the perturbation is large. The possible extension of this result to wider classes of equations is discussed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1703931