Discrete Petrov-Galerkin scheme for boundary value differential and integral problems: Theory and applications

Mathematical and Computer Modelling

Volumn 40, Issue 11-12, 2004, Pages 1323-1334

  Ganesh, M ^a   Grigorieff, R D ^b   Mustapha, K ^c  

^a Department of Metallurgical and Materials Engineering   (United States)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Discrete Petrov Galerkin method; Integrodifferential equations; Nonlinear differential equations; Nonlinear side conditions; Singularly perturbed problems

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GALERKIN METHODS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DISCRETE PETROV GALERKIN SCHEMES; MESH RESTRICTIONS; NONLINEAR SIDE CONDITIONS; OPTIMAL ORDER CONVERGENCE;

BOUNDARY VALUE PROBLEMS;

EID: 18044371882     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.01.022     Document Type: Article

References (13)

1. M. Ganesh, and I.H. Sloan Optimal order spline methods for nonlinear differential and integro-differential equations Appl. Numer. Math. 29 1999 445 478
2. R.D. Grigorieff, and I.H. Sloan Stability of discrete orthogonal projections for continuous splines Bull. Austral. Math. Soc. 58 1998 307 332
3. U.M. Ascher, R.M.M. Mattheij, and R.D. Russell Numerical Solution of Boundary Value Problems for Ordinary Differential Equations 1995 SIAM New York
4. U.M. Ascher, J. Christiansen, and R.D. Russell Collocation software for boundary-value ODEs ACM Trans. Math. Software 7 1981 209 222
5. U.M. Ascher, J. Christiansen, and R.D. Russell COLSYS--A collocation code for boundary value problems B. Childs Lecture Notes Comp. Sci. Vol. 76 1979 Springer-Verlag Philadelphia, PA 164 185
6. G. Bader, and U. Ascher A new basis implementation for a mixed order boundary value ODE solver SIAM J. Scient. Stat. Comput. 8 1987 483 500
7. C. de Boor, and B. Swartz Collocation at Gaussian points SIAM J. Numer. Anal. 10 1973 582 606
8. G. Vainikko Approximate methods for nonlinear equations (two approaches to the convergence problem) Nonlinear Analysis TMA 2 1978 647 687
9. J.R. Cash A comparison of some global methods for solving two point-boundary value problems Appl. Math. Comput. 31 1989 449 462
10. J.R. Cash, and M.H. Wright A deferred correction method for nonlinear two-point boundary value problems: Implementation and numerical evaluation SIAM J. Sci. Stat. Comput. 12 1991 971 989
11. P.W. Hemker A Numerical Study of Stiff Two-Point Boundary Value Problems 1977 Mathematisch Centrum New York
12. M. Ganesh, and A. Spense Orthogonal collocation for a nonlinear integro-differential equations IMA J. Numer. Anal. 18 2 1998 191 206
13. R.J. Hangelbroek, H.G. Kaper, and G.K. Leaf Collocation methods for integro-differential equations SIAM J. Numer. Anal. 14 1977 377 390