A subdivision approach to the construction of approximate solutions of boundary-value problems with deviating arguments

Computers and Mathematics with Applications

Volumn 35, Issue 11, 1998, Pages 121-135

  Qu, R ^a   Agarwal, R P ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Approximation; Boundary value problem; Delay differential equation; Interpolation; Iterative method; Method of collocation; Subdivision algorithm

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; INTERPOLATION; ITERATIVE METHODS; NONLINEAR EQUATIONS;

COLLOCATION METHOD; DELAY DIFFERENTIAL EQUATION; SUBDIVISION ALGORITHM;

BOUNDARY VALUE PROBLEMS;

EID: 0032091995     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00089-3     Document Type: Article

References (19)

1. R.P. Agarwal and Y.M. Chow, Finite-difference methods for boundary-value problems of differential equations with deviating arguments, Computers Math. Applic. 12 (11), 1143-1153, (1986).
2. R.P. Agarwal, Existence-uniqueness and iterative methods for right focal point boundary-value problems for differential equations with deviating arguments, Annales Polonici Mathematici 52, 211-230, (1991).
3. R.P. Agarwal and Q. Sheng, Right focal point boundary-value problems for functional-differential equations, In Boundary Value Problems for Functional Differential Equations, (Edited by J. Henderson), pp. 1-12, World Scientific, (1995).
4. st Mat. Univ. Trieste 11, 32-46, (1979).
5. F.J. Burkowski and D.D. Cowan, The numerical derivation of a periodic solution of a second order differential difference equation, SIAM J. Numer. Analysis 10, 489-49, (1973).
6. P. Chocholaty and L. Slahor, A numerical method to boundary value problems for second order delay differential equations, Numer. Analysis 33, 69-75, (1979).
7. L.E. El'sgol'ts, Introduction to the Theory of Differential Equations with Deviating Arguments, Holden Day, San Francisco, CA, (1966).
8. L. Grimm and K. Schmitt, Boundary value problems for differential equations with deviating arguments, Aequationes Math. 3, 24-38, (1969).
9. R.K. Jain and R.P. Agarwal, Finite difference method for second order functional differential equations, J. Math. Phys. Sci. 7, 301-306, (1973).
10. K. DeNevers and K. Schmitt, An application to shooting method to boundary value problems for second order delay equations, J. Math. Anal. Appl. 36, 588-597, (1971).
11. G.W. Reddien and C.C. Travis, Approximation methods for boundary value problems of differential equations with functional arguments, J. Math. Anal. Appl. 46, 62-74, (1974).
12. K. Schmitt, On solutions of nonlinear differential equations with deviating arguments, SIAM J. Appl. Math. 17, 1171-1176, (1969).
13. R.P. Agarwal, The method of complementary functions for nonlinear boundary value problems, J. Optimization Theory Applic. 36, 139-144, (1982).
14. R.P. Agarwal, Initial-value method for discrete boundary value problems, J. Math. Anal. Appl. 100, 513-529, (1984).
15. R.P. Agarwal and R.C. Gupta, Method of chasing for multipoint boundary value problems, Appl. Math. Comput. 17, 37-43, (1985).
16. R. Qu and R.P. Agarwal, Solving two point boundary value problems by interpolatory subdivision algorithms, Int. J. Computer Mathematics 60, 279-294, (1996).
17. R. Qu and R.P. Agarwal, An iterative scheme for solving nonlinear two point boundary value problems (to appear).
18. R. Qu and R.P. Agarwal, A cross difference approach to the analysis of subdivision algorithms, Neural, Parallel & Scientific Computations 3, 393-416, (1995).
19. R. Qu, New formulae for numerical differentiation and integration, Mathl. Comput. Modelling 24 (10), 55-68, (1996).