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Mathematics of Computation

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Quadrature methods for integral equations of the second kind over infinite intervals

Author: Ian H. Sloan
Journal: Math. Comp. 36 (1981), 511-523
MSC: Primary 65R20; Secondary 45B05
MathSciNet review: 606510
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Abstract: Convergence results are proved for a class of quadrature methods for integral equations of the form $ y(t) = f(t) + \smallint _0^\infty \;k(t,s)y(s)\,ds$. An important special case is the Nyström method, in which the integral term is approximated by an ordinary quadrature rule. For all of the methods considered here, the rate of convergence is the same, apart from a constant factor, as that of the quadrature approximation to the integral term.

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Keywords: Integral equation, Fredholm equation, equation of the second kind, infinite interval, Nyström method, quadrature method
Article copyright: © Copyright 1981 American Mathematical Society

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