A collocation method with cubic splines for multidimensional weakly singular nonlinear integral equations

Journal of Integral Equations and Applications

Volumn 6, Issue 2, 1994, Pages 257-266

  Uba, Peep ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040891771     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075807     Document Type: Article

References (9)

1. H. Kaneko, R. Noren and Y. Xu, Regularity of the solution of Hammerstein equations with weakly singular kernel, Integral Equations Operator Theory (1990) 13, 660-670.
2. H. Kaneko, R. Noren and Y. Xu, Numerical solution for weakly singular Hammerstein equations and their superconvergence, J. Integral Equation Appl. 4 (1992), 391-407.
3. M. Krasnoselskii, G. Vainikko, P. Zabreiko, Ya. Rutitskii and V. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff, Groningen, 1972.
4. J. R. Rice, On the degree of convergence of nonlinear spline approximation, in Approximations with special emphasis on spline functions, Academic Press, New York, 1969.
5. Yu. Savyalov, B. Kvasov and V. Miroshnichenko, The spline-function method, (Russian) Moscow, 1980.
6. P. Uba, A collocation method with cubic splines to the solution of a multidimensional weakly singular integral equation, Acta et Commentationes Universitatis Tartuensis 863 Tartu, 1989, 19-25.
7. P. Uba, On the convergence of interpolate cubic splines on non-uniform grids, (Russian) Proceeding of the Estonian Academy of Sciences, Physics-Mathematics 31 (1982), 393-409.
8. G. Vainikko, Estimations of derivatives of a solution to a nonlinear weakly singular integral equation, in Problems of pure and applied mathematics, Abstract of conference, Tartu, 1990, 212-215.
9. G. Vainikko, Multidimensional weakly singular integral equations, Lect. Notes Math. 1549, Springer-Verlag, 1993.