Integral equations on the half-line: a modified finite-section approximation

Authors:
I. H. Sloan and A. Spence

Journal:
Math. Comp. **47** (1986), 589-595

MSC:
Primary 65R20; Secondary 45L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856704-0

MathSciNet review:
856704

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Abstract: We consider the approximate solution of integral equations of the form , where the conditions on are such that kernels of the Wiener-Hopf form are included in the analysis. The finite-section approximation, in which the infinite integral is replaced by for some , yields an approximate solution that is known, under very general conditions, to converge to as with *t* fixed. However, the convergence is uniform only on finite intervals, and the approximation is typically very poor for . Under the assumption that *f* has a limit at infinity, we here introduce a modified finite-section approximation with improved approximation properties, and prove that the new approximate solution converges uniformly to *y* as . A numerical example illustrates the improvement.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0856704-0

Article copyright:
© Copyright 1986
American Mathematical Society