Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels

Journal of Computational and Applied Mathematics

Volumn 213, Issue 1, 2008, Pages 111-126

  Pedas, Arvet ^a   Tamme, Enn ^a  

^a UNIVERSITY OF TARTU   (Estonia)

Author keywords

Discrete Galerkin method; Graded grid; Weakly singular integro differential equation

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; INTEGRAL EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

DISCRETE GALERKIN METHOD; GRADED GRID; WEAKLY SINGULAR INTEGRO-DIFFERENTIAL EQUATION;

GALERKIN METHODS;

EID: 37549001375     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.12.024     Document Type: Article

References (15)

1. K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge Monographs on Applied and Computational Mathematics, vol. 4, Cambridge University Press, Cambridge, UK, 1997.
2. Atkinson K., and Bogomolny A. The discrete Galerkin method for integral equations. Math. Comp. 48 (1987) 596-616
3. H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge Monographs on Applied and Computational Mathematics, vol. 15, Cambridge University Press, Cambridge, UK, 2004.
4. Brunner H., Pedas A., and Vainikko G. The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Math. Comp. 68 (1999) 1079-1095
5. Brunner H., Pedas A., and Vainikko G. Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. SIAM J. Numer. Anal. 39 (2001) 957-982
6. Chen Z., Xu Y., and Zhao J. The discrete Petrov-Galerkin method for weakly singular integral equations. J. Integral Equations Appl. 11 (1999) 1-35
7. Ganesh M., Grigorieff R.D., and Mustapha K. Discrete Petrov-Galerkin Scheme for boundary value differential and integral problems: theory and applications. Math. Comput. Modelling 40 (2004) 1323-1334
8. Ganesh M., and Sloan I.H. Optimal order spline methods for nonlinear differential and integro-differential equations. Appl. Numer. Math. 29 (1999) 445-478
9. Grigorieff R.D., and Sloan I.H. High-order spline Petrov-Galerkin methods with quadrature. Z. Angew. Math. Mech. 76 1 (1996) 15-18
10. Grigorieff R.D., and Sloan I.H. Stability of discrete orthogonal projections for continuous splines. Bull. Austral. Math. Soc. 58 (1998) 307-332
11. Parts I., Pedas A., and Tamme E. Piecewise polynomial collocation for Fredholm integro-differential equations with weakly singular kernels. SIAM J. Numer. Anal. 43 (2005) 1897-1911
12. Pedas A., and Tamme E. Spline collocation method for integro-differential equations with weakly singular kernels. J. Comput. Appl. Math. 197 (2006) 253-269
13. Pedas A., and Vainikko G. Smooting transformation and piecewise polynomial collocation for weakly singular Volterra integral equations. Computing 73 (2004) 271-293
14. Pedas A., and Vainikko G. Smooting transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Comm. Pure Appl. Anal. 5 (2006) 395-413
15. G. Vainikko, Multidimensional Weakly Singular Integral Equations, Lecture Notes in Mathematics, vol. 1549, Springer, Berlin, 1993.