Sinc-collocation methods for weakly singular Fredholm integral equations of the second kind

Journal of Computational and Applied Mathematics

Volumn 234, Issue 4, 2010, Pages 1211-1227

  Okayama, Tomoaki ^a   Matsuo, Takayasu ^a   Sugihara, Masaaki ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Fredholm integral equation; Sinc approximation; Smoothing transformation; Weakly singular kernel

Indexed keywords

EXPONENTIAL CONVERGENCE; FREDHOLM INTEGRAL EQUATIONS; NUMERICAL EXAMPLE; SINC-COLLOCATION METHOD; SMOOTHING TRANSFORMATION; WEAKLY SINGULAR; WEAKLY SINGULAR KERNEL;

INTEGRAL EQUATIONS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77950341700     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.07.049     Document Type: Article

References (25)

1. Schneider C. Regularity of the solution to a class of weakly singular Fredholm integral equations of the second kind. Integral Equations Operator Theory 2 (1979) 62-68
2. Schneider C. Product integration for weakly singular integral equations. Math. Comput. 36 (1981) 207-213
3. Ren Y., Zhang B., and Qiao H. A simple Taylor-series expansion method for a class of second kind integral equations. J. Comput. Appl. Math. 110 (1999) 15-24
4. Richter G.R. On weakly singular Fredholm integral equations with displacement kernels. J. Math. Anal. Appl. 55 (1976) 32-42
5. Vainikko G., and Pedas A. The properties of solutions of weakly singular integral equations. J. Aust. Math. Soc. Ser. B 22 (1981) 419-430
6. Graham I.G. Singularity expansions for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels. J. Integral Equations 4 (1982) 1-30
7. Graham I.G. Galerkin methods for second kind integral equations with singularities. Math. Comput. 39 (1982) 519-533
8. Vainikko G., and Uba P. A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel. J. Austral. Math. Soc. Ser. B 22 (1981) 431-438
9. Baratella P. A note on the convergence of product integration and Galerkin method for weakly singular integral equations. J. Comput. Appl. Math. 85 (1997) 11-18
10. Monegato G., and Scuderi L. High order methods for weakly singular integral equations with nonsmooth input functions. Math. Comput. 67 (1998) 1493-1515
11. Galperin E.A., Kansa E.J., Makroglou A., and Nelson S.A. Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations. J. Comput. Appl. Math. 115 (2000) 193-211
12. Pedas A., and Vainikko G. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Commun. Pure Appl. Anal. 5 (2006) 395-413
13. Vainikko E., and Vainikko G. A spline product quasi-interpolation method for weakly singular Fredholm integral equations. SIAM J. Numer. Anal. 46 (2008) 1799-1820
14. Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind (1997), Cambridge University Press, New York
15. Kythe P.K., and Puri P. Computational Methods for Linear Integral Equations (2002), Birkhäuser, Boston
16. Riley B.V. The numerical solution of Volterra integral equations with nonsmooth solutions based on sinc approximation. Appl. Numer. Math. 9 (1992) 249-257
17. Brunner H. Collocation Methods for Volterra Integral and Related Functional Equations (2004), Cambridge University Press, Cambridge
18. Stenger F. Numerical Methods Based on Sinc and Analytic Functions (1993), Springer-Verlag, New York
19. Mori M., and Sugihara M. The double-exponential transformation in numerical analysis. J. Comput. Appl. Math. 127 (2001) 287-296
20. Sugihara M., and Matsuo T. Recent developments of the Sinc numerical methods. J. Comput. Appl. Math. 164/165 (2004) 673-689
21. Tanaka K., Sugihara M., and Murota K. Function classes for successful DE-Sinc approximations. Math. Comput. 78 (2009) 1553-1571
22. T. Okayama, T. Matsuo, M. Sugihara, Error estimates with explicit constants for Sinc approximation, Sinc quadrature and Sinc indefinite integration, Mathematical Engineering Technical Reports 2009-01, The University of Tokyo, 2009
23. Rudin W. Real and Complex Analysis. 3rd ed. (1987), McGraw-Hill, New York
24. Baratella P., and Orsi A.P. A new approach to the numerical solution of weakly singular Volterra integral equations. J. Comput. Appl. Math. 163 (2004) 401-418
25. M. Rasty, M. Hadizadeh, A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations, Acta Appl. Math. (in press)