Journal of Integral Equations and Applications

A Collocation Method with Cubic Splines for Multidimensional Weakly Singular Nonlinear Integral Equations

Peep Uba

Full-text: Open access

Article information

J. Integral Equations Applications Volume 6, Number 2 (1994), 257-266.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Uba, Peep. A Collocation Method with Cubic Splines for Multidimensional Weakly Singular Nonlinear Integral Equations. J. Integral Equations Applications 6 (1994), no. 2, 257--266. doi:10.1216/jiea/1181075807.

Export citation


  • 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.
  • --------, Numerical solution for weakly singular Hammerstein equations and their superconvergence, J. Integral Equation Appl. 4 (1992), 391-407.
  • M. Krasnoselskii, G. Vainikko, P. Zabreiko, Ya. Rutitskii and V. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff, Groningen, 1972.
  • 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.
  • Yu. Sav'yalov, B. Kvasov and V. Miroshnichenko, The spline-function method, (Russian) Moscow, 1980.
  • P. Uba, A collocation method with cubic splines to the solution of a multi-dimensional weakly singular integral equation, Acta et Commentationes Universitatis Tartuensis 863 Tartu, 1989, 19-25.
  • --------, 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.
  • 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.
  • --------, Multidimensional weakly singular integral equations, Lect. Notes Math. 1549, Springer-Verlag, 1993.