The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

Applied Numerical Mathematics

Volumn 57, Issue 3, 2007, Pages 253-269

  Wang, Yuan Ming ^a,b  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b SHANGHAI NORMAL UNIVERSITY   (China)

Author keywords

Asymptotic error expansion; Nonlinear two point boundary value problem; Numerov's method; Richardson's extrapolation

Indexed keywords

BOUNDARY CONDITIONS; ERROR ANALYSIS; EXTRAPOLATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

ASYMPTOTIC ERROR EXPANSION; NONLINEAR TWO POINT BOUNDARY VALUE PROBLEMS; NUMEROV'S METHODS; RICHARDSON EXTRAPOLATION;

ALGORITHMS;

EID: 33846794751     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2006.02.009     Document Type: Article

References (32)

1. n: Part II: Applications. Nonlinear Anal. 5 (1981) 525-542
2. Agarwal R.P. On Numerov's method for solving two point boundary value problems. Utilitas Math. 28 (1985) 159-174
3. Agarwal R.P. Difference Equations and Inequalities (1992), Marcel Dekker, New York
4. Agarwal R.P., and Wang Y.-M. Some recent developments of the Numerov's method. Computers Math. Appl. 42 3-5 (2001) 561-592
5. Ames W.F. Nonlinear Partial Differential Equations in Engineering (1972), Academic Press, New York
6. Ames W.F. Numerical Methods for Partial Differential Equations (1977), Academic Press, New York
7. Aris R. The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (1975), Clarendon Press, Oxford
8. Aronson D.G., and Weinberger H.F. Nonlinear diffusion in population genetics, combustion, and nerve propagation. Partial Differential Equations and Related Topics. Lecture Notes in Mathematics vol. 446 (1975), Springer, New York 5-49
9. Chan R.P.K., Leone P., and Tsai A. Order conditions and symmetry for two-step hybrid methods. Int. J. Computer Math. 81 (2004) 1519-1536
10. Chawla M.M., and Shivakumar P.N. Numerov's method for non-linear two-point boundary value problems. Int. J. Computer Math. 17 (1985) 167-176
11. Chawla M.M., and Subramanian R. A new fourth order cubic spline method for nonlinear two-point boundary value problems. Int. J. Computer Math. 22 (1987) 321-341
12. ″ = f (x, y). IMA J. Numer. Anal. 23 (2003) 197-220
13. Collatz L. The Numerical Treatment of Differential Equations. third ed. (1960), Springer, Berlin
14. Dahlquist G., and Bjorck A. Numerical Methods (1974), Prentice-Hall, Englewood Cliffs, NJ
15. Guo B.-Y., and Miller J.J.H. Iterative and Petrov-Galerkin methods for solving a system of one-dimensional nonlinear elliptic equations. Math. Comp. 58 (1992) 531-547
16. Henrici P. Discrete Variable Methods in Ordinary Differential Equations (1962), John Wiley, New York
17. Lees M. Discrete methods for nonlinear two-point boundary value problems. In: Bramble J.H. (Ed). Numerical Solution of Partial Differential Equations (1966), Academic Press, New York 59-72
18. Marchuk G.I., and Shaidurov V.V. Difference Methods and Their Extrapolations (1983), Springer, New York
19. Morton K.W. Numerical Solution of Convection-Diffusion Problems (1996), Chapman & Hall, London, UK
20. Numerov B.V. A method of extrapolation of perturbations. Roy. Ast. Soc. Monthly Notices 84 (1924) 592-601
21. Ortega J.M., and Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables (1976), Academic Press, New York
22. Pao C.V. Nonlinear Parabolic and Elliptic Equations (1992), Plenum Press, New York
23. Pryce J.D. Numerical Solutions of Sturm-Liouville Problems (1993), Clarendon Press, Oxford
24. Wang J. Monotone method for diffusion equations with nonlinear diffusion coefficients. Nonlinear Anal. 34 (1998) 113-142
25. Wang J., and Pao C.V. Finite difference reaction-diffusion equations with nonlinear diffusion coefficients. Numer. Math. 85 (2000) 485-502
26. Wang Y.-M. Monotone methods for a boundary value problem of second-order discrete equation. Computers Math. Appl. 36 6 (1998) 77-92
27. Wang Y.-M. Accelerated monotone iterative methods for a boundary value problem of second-order discrete equations. Computers Math. Appl. 39 3/4 (2000) 85-94
28. Wang Y.-M. Numerov's method for strongly nonlinear two-point boundary value problems. Computers Math. Appl. 45 (2003) 759-763
29. Wang Y.-M., and Agarwal R.P. Monotone methods for solving a boundary value problem of second order discrete system. Mathematical Problems in Engineering: Theory, Methods and Applications 5 (1999) 291-315
30. Wang Y.-M., and Guo B.-Y. On Numerov scheme for nonlinear two-points boundary value problem. J. Comput. Math. 16 (1998) 345-366
31. Wang Y.-M., and Guo B.-Y. Petrov-Galerkin methods for nonlinear systems without monotonicity. Appl. Numer. Math. 36 (2001) 57-78
32. Wang Y.-M., and Guo B.-Y. Monotone finite difference schemes for nonlinear systems with mixed quasi-monotonicity. J. Math. Anal. Appl. 267 (2002) 599-625