A collocation method for Fredholm integral equations of the second kind
Authors:
E. N. Houstis and T. S. Papatheodorou
Journal:
Math. Comp. 32 (1978), 159173
MSC:
Primary 65R05; Secondary 45B05
MathSciNet review:
0458967
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Abstract: An interpolation scheme based on piecewise cubic polynomials with Gaussian points as interpolation points is analyzed and applied to the solution of Fredholm equations of the second kind.
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 K. E. ATKINSON, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, Dept. of Math., Univ. of Iowa publication. MR 0483585 (58:3577)
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 JIM DOUGLAS, JR. & TODD DUPONT, "A super convergence result for the approximate solution of the heat equation by a collocation method," The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), Academic Press, New York, 1972. MR 0373329 (51:9529)
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 E. N. HOUSTIS, "A collocation method for systems of nonlinear ordinary differential equations," J. Math. Anal. Appl., v. 61, 1978. MR 0488785 (58:8295)
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 E. N. HOUSTIS, "Application of method of collocation on lines for solving nonlinear hyperbolic problems," Math. Comp., v. 31, 1977, pp. 443456. MR 0443379 (56:1749)
 [11]
 E. N. HOUSTIS, "Collocation methods for linear elliptic problems," Math. Comp. (To appear.) MR 508331 (80a:65237)
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 E. N. HOUSTIS & T. S. PAPATHEODOROU, Piecewise Cubic Hermite Interpolation at the Gaussian Points, Purdue University, CSDTR 199, July 1976.
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 M. H. SCHULTZ, Spline Analysis, PrenticeHall, Englewood Cliffs, N. J., 1973. MR 0362832 (50:15270)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804589678
PII:
S 00255718(1978)04589678
Keywords:
Collocation method,
integral equations
Article copyright:
© Copyright 1978
American Mathematical Society
