Instability of invariant boundary conditions of a generalized Lane-Emden equation of the second-kind

Applied Mathematics and Computation

Volumn 198, Issue 2, 2008, Pages 621-633

  Harley, C ^a   Momoniat, E ^a  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

Invariant boundary condition; Lane Emden equation; Lie group method; Phase plane analysis; Stability

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

ARBITRARY SHAPE FACTORS; INVARIANT BOUNDARY CONDITIONS; LIE POINT SYMMETRIES; PHASE PLANE ANALYSIS;

BOUNDARY CONDITIONS;

EID: 40849113611     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.08.077     Document Type: Article

References (23)

1. Ascher U.M., Mattheij R.M.M., and Russell R.D. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations (1995), SIAM
2. Balakrishnan E., Swift A., and Wake G.C. Critical values for some non-class A geometries in thermal ignition theory. Math. Comput. Modell. 24 (1996) l-10
3. Barenblatt G.I., Bell J.B., and Crutchfield W.Y. The thermal explosion revisited. Proc. Natl. Acad. Sci. USA 95 (1998) 13384-13386
4. Binney J., and Tremaine S. Galactic Dynamics (1987), Princeton University Press, Princeton
5. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer, Berlin
6. Bonnor W.B. Boyle's law and gravitational instability. MNRAS 11 (1956) 351-359
7. Bozkhov Y., and Martins A.C.G. Lie point symmetries and exact solutions of quasilinear differential equations with critical exponents. Nonlinear Anal. 57 (2004) 773-793
8. Chambré P.L. On the solution of the Poisson-Boltzmann equation with application to the theory of thermal explosions. J. Chem. Phys. 20 (1952) 1795-1797
9. Chandrasekhar S. An Introduction to the Study of Stellar Structure (1939), Dover Publications Inc.
10. Dresner L. Phase-plane analysis of nonlinear, second-order, ordinary differential equations. J. Math. Phys. 12 (1971) 1339-1348
11. Emden R. Gaskugeln - Anwendungen der Mechan. Warmtheorie (1907), Druck und Verlag Von B. G. Teubner, Leipzig and Berlin
12. Frank-Kamenetzkii D.A. Diffusion and Heat Transfer in Chemical Kinetics (1969), Plenum Press, New York
13. Ibragimov N.H. CRC Handbook of Lie Group Analysis of Differential Equations vol. 1 (1994), CRC Press Inc., Boca Raton, FL
14. Ibragimov N.H. CRC Handbook of Lie Group Analysis of Differential Equations vol. 2 (1995), CRC Press Inc., Boca Raton, FL
15. Ibragimov N.H. Elementary Lie Group Analysis and Ordinary Differential Equations (1999), J. Wiley and Sons, Chichester
16. Kippenhahn R., and Weigert A. Stellar Structure and Evolution (1990), Springer-Verlag, Berlin
17. Momoniat E., and Harley C. Approximate implicit solution of a Lane-Emden equation. New Astron. 11 (2006) 520-526
18. E. Noether, Invariante Variationsprobleme, König. Gesell. Wissen Göttingen, Math.-Phys. Kl. Heft 2 (1918).
19. Ovsiannikov L.V. Group Analysis of Differential Equations (1982), Academic Press, New York
20. Richardson O.W. Emission of Electricity from Hot Bodies (1921), Longman, New York
21. Russell R.D., and Shampine L.F. Numerical methods for singular boundary value problems. SIAM J. Numer. Anal. 12 (1975) 13-36
22. L.F. Shampine, M.W. Reichelt, J. Kierzenka, Solving Boundary Value Problems for Ordinary Differential Equations in MATLAB with bvp4c. .
23. Wazwaz A.-M. A new algorithm for solving differential equations of Lane-Emden type. Appl. Math. Comput. 118 (2001) 287-310