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Mathematics of Computation

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Cubic splines and approximate solution of singular integral equations

Authors: Erica Jen and R. P. Srivastav
Journal: Math. Comp. 37 (1981), 417-423
MSC: Primary 65R20; Secondary 41A15, 45E05
MathSciNet review: 628705
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Abstract: Of concern here is the numerical solution of singular integral equations of Cauchy type; i.e., equations involving principal value integrals. The unknown function is expressed as the product of an appropriate weight function and a cubic spline. The problem is reduced to a system of linear algebraic equations which is solved for the approximate values of the function at the knots. An estimate is provided for the maximum error of the approximate solution. Numerical results from the spline method are compared with those obtained using other methods.

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Keywords: Spline approximation, numerical solution of singular integral equations
Article copyright: © Copyright 1981 American Mathematical Society