Cubic splines and approximate solution of singular integral equations
Authors:
Erica Jen and R. P. Srivastav
Journal:
Math. Comp. 37 (1981), 417423
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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 F. Erdogan & G. D. Gupta, "On the numerical solution of singular integral equation," Quart. Appl. Math., v. 30, 1972, pp. 525534. MR 0408277 (53:12042)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106287054
PII:
S 00255718(1981)06287054
Keywords:
Spline approximation,
numerical solution of singular integral equations
Article copyright:
© Copyright 1981
American Mathematical Society
