Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T06:06:52.360Z Has data issue: false hasContentIssue false
  • English
  • Français

A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel

Published online by Cambridge University Press:  17 February 2009

G. Vainikko  and
P. Uba
G. Vainikko
Affiliation:
Department of Applied Mathematics, Tartu State University, 202 400, Tartu, Liivi 2, U.S.S.R.
P. Uba
Affiliation:
Department of Applied Mathematics, Tartu State University, 202 400, Tartu, Liivi 2, U.S.S.R.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct collocation methods with an arbitrary degree of accuracy for integral equations with logarithmically or algebraically singular kernels. Superconvergence at collocation points is obtained. A grid is used, the degree of non-uniformity of which is in good conformity with the smoothness of the solution and the desired accuracy of the method.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 4 , April 1981 , pp. 431 - 438
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Krasnosel'skii, M. A., Vainikko, G. M., Zabreiko, P. P., Rutitskii, Ya. B. and Stetsenko, V. Ya., Approximate solution of operator equations (Wolters-Noordhoff, 1972).CrossRefGoogle Scholar
[2]Pedas, A., “Piecewise linear approximation of solution of integral equation with logarithmical singular kernel”, Tartu Riikl. Ul. Toimetised, Vih. 500 (1979), 33–42.Google Scholar
[3]Rice, J. R., “On the degree of convergence of nonlinear spline approximation”, in Approximations with special emphasis on spline functions (Academic Press, New York, 1969).Google Scholar
[4]Vainikko, G. and Pedas, A., “The properties of solutions of weakly singular integral equations”, J. Austral. Math. Soc. B 22 (1981), 419–430.CrossRefGoogle Scholar
[5]Vainikko, G. and Uba, P., “A piecewise polynomial approximation to the solution of an integral equation with weak singularity”, in theses of conference Theoretical and applied problems of mathematics, Tartu (1980), 196–198.Google Scholar