Piecewise quasilinearization techniques for singular boundary-value problems

Computer Physics Communications

Volumn 158, Issue 1, 2004, Pages 12-25

  Ramos, J I ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Boundary value problems; Lane Emden equation; Quasilinearization methods; Singular ordinary differential equations; Thomas Fermi equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; FLUID DYNAMICS; ITERATIVE METHODS; LINEARIZATION; ORDINARY DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; QUANTUM THEORY;

LANE-EMDEN EQUATION; QUASILINEARIZATION METHODS; SINGULAR ORDINARY DIFFERENTIAL EQUATIONS; THOMAS-FERMI EQUATION;

BOUNDARY VALUE PROBLEMS;

EID: 1142304425     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comphy.2003.11.003     Document Type: Article

References (24)

1. Jamet P. On the convergence of difference approximations to one-dimensional singular boundary value problems. SIAM J. Numer. Anal. 14:1970;355-378.
2. Chawla M.M., Katti C.P. A finite-difference method for a class of singular boundary-value problems. IMA J. Numer. Anal. 4:1984;457-466.
3. 2 method for a singular two point boundary value problem. BIT. 26:1986;318-326.
4. Kumar M. A fourth-order finite difference method for a class of singular two-point boundary value problems. Appl. Math. Comput. 133:2002;539-545.
5. Kumar M. A three-point finite difference method for a class of singular two-point boundary value problems. J. Comput. Appl. Math. 145:2002;89-97.
6. Ciarlet P.G., Natterer F., Varga R.S. Numerical methods of high order accuracy for singular nonlinear boundary-value problems. Numer. Math. 15:1970;87-99.
7. Iyengar S.R.K., Jain P. Spline methods for singular two-point boundary-value problems. Numer. Math. 50:1987;363-376.
8. Mandelzweig V.B., Tabakin F. Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs. Comput. Phys. Commun. 141:2001;268-281.
9. Lima P.M., Carpentier M. Numerical solution of a singular boundary-value problem in non-Newtonian fluid mechanics. Comput. Phys. Comm. 126:2000;114-120.
10. Frommlet F., Weinmüller E.B. On asymptotic error expansions for singular boundary value problems. Math. Models Methods Appl. Sci. 11:2001;71-85.
11. Koch O., Weinmüller E.B. The convergence of shooting methods for singular boundary value problems. Math. Comput. 72:2003;289-305.
12. Koch O., Kofler P., Weinmüller E.B. The implicit Euler method for the numerical solution of singular initial value problems. Appl. Numer. Math. 34:2000;231-252.
13. Koch O., Kofler P., Weinmüller E.B. Initial value problems for systems of ordinary first and second order differential equations with a singularity of the first kind. Analysis. 21:2001;373-389.
14. Koch O., Weinmüller E.B. Iterated defect correction for the solution of singular initial value problems. SIAM J. Numer. Anal. 38:2001;1784-1799.
15. Ramos J.I., García-López C.M. Linearized θ -methods. I. Ordinary differential equations. Comput. Methods Appl. Mech. Engrg. 129:1996;255-269.
16. Ramos J.I. Maps of implicit, linearized θ -methods for the logistic differential equation. Appl. Math. Comput. 94:1998;1-15.
17. Ramos J.I. Linearized methods for ordinary differential equations. Appl. Math. Comput. 104:1999;109-129.
18. Ramos J.I. A piecewise time-linearized method for the logistic differential equation. Appl. Math. Comput. 93:1998;139-148.
19. Ramos J.I., García-López C.M. Piecewise-linearized methods for initial-value problems. Appl. Math. Comput. 82:1997;459-467.
20. Ramos J.I. Linearization methods in classical and quantum mechanics. Comput. Phys. Comm. 153:2003;199-208.
21. Allen D.N. de G., Southwell R.V. Relaxation methods applied to motion, in two dimensions, of a viscous fluid past a fixed cylinder. Quarterly J. Mechanics Appl. Math. 8:1955;129-145.
22. Il'in A.M. A difference scheme for a differential equation with a small parameter affecting the highest derivative. Math. Zam. 6:1969;237-248.
23. Ramos J.I. On diffusive and exponentially fitted techniques. Appl. Math. Comput. 103:1999;69-96.
24. Bethe H.A., Jackiw R.W. Intermediate Quantum Mechanics. 1968;W.A. Benjamin, Inc. New York.