Chebyshev spectral collocation methods for nonlinear isothermal magnetostatic atmospheres

Journal of Computational and Applied Mathematics

Volumn 115, Issue 1-2, 2000, Pages 309-329

  Khater, A H ^a   Shamardan, A B ^b   Callebaut, D K ^c   Ibrahim, R S ^a  

^a Beni Suef University   (Egypt)

^b El Minia University ^*  (Egypt)

^c UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Chebyshev spectral collocation methods; Isothermal magnetostatic atmospheres; Nonlinear elliptic boundary value problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; CHEBYSHEV APPROXIMATION; CURRENT DENSITY; FINITE DIFFERENCE METHOD; MAGNETIC FLUX; MAGNETOHYDRODYNAMICS; MAGNETOSTATICS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; SPECTRUM ANALYSIS;

CHEBYSHEV SPECTRAL COLLOCATION METHODS; GRAD-SHAFRANOV EQUATION; ISOTHERMAL MAGNETOSTATIC ATMOSPHERES; NONLINEAR ELLIPTIC EQUATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0034159704     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00306-4     Document Type: Article

References (19)

1. Amari T., Aly J.J. Two-dimensional isothermal magnetostatic equilibria in a gravitational field. Astron. Astrophys. 208:1989;361.
2. Birn J., Goldstein H., Schindler K. A theory of the onset of solar eruptive processes. Solar Phys. 57:1978;81.
3. C. Canuto, M.Y. Hussaini, A. Quarterani, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, 1988.
4. El-gendi S.E. Chebyshev solution of differential, integral and integro-differential equations. Comput. J. 12:1969;282.
5. D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1977.
6. Haidvogel D.B. Resolution of downstream boundary layers in the Chebyshev approximation to viscous flow problems. J. Comput. Phys. 33:1979;313.
7. J. Heyvaerts, J.M. Larsy, M. Schatzman, P. Witomsky, A mathematical model of solar flares, Quart. Appl. Math. XLI (1983) 1.
8. Karageorghis A., Phillips T.N. Chebyshev spectral collocation method for laminar flow through a channal contraction. J. Comput. Phys. 84:1989;114.
9. Khater A.H. Analytical solutions for some nonlinear magnetostatic atmosphere. Astrophys. Sp. Sci. 162:1989;151.
10. Khater A.H., Callebaut D.K., Ibrahim R.S. Bäcklund transformations and painlevé analysis: exact solutions for the nonlinear isothermal magnetostatic atmospheres. Phys. Plasmas. 4:1997;2853.
11. A.H. Khater, D.K. Callebaut, R.S. Ibrahim, O.H. El-Kalaawy, Bäcklund transformations and exact soliton solutions for nonlinear evolution equations of the ZS AKNS system, Chaos, Solitons & Fractals 8 (1998) 1847.
12. Khater A.H., Callebaut D.K., Kamel E.S. Painlevé analysis and exact solution for an isothermal magnetic atmosphere. Solar Phys. 178:1998;285.
13. A.H. Khater, O.H. El-Kalaawy, D.K. Callebaut, Bäcklund transformations and exact solutions for nonlinear elliptic equation modelling isothermal magnetostatic atmosphere, IMA J. Appl. Math., in press, 1998.
14. Khater A.H., Ibrahim R.S., Shamardan A.B., Callebaut D.K. Bäcklund transformations and painlevé analysis: exact solutions for a Grad-Shafranov type magnetohydrodynamic equilibrium. IMA J. Appl. Math. 58:1997;51.
15. Low B.C., Hundhausen J.A., Zweibel E.G. Nonlinear periodic solutions for the isothermal magnetostatic atmosphere. Phys. Fluids. 26:1983;2731.
16. Orszag S.A. Spectral methods for problems in complex geometries. J. Comput. Phys. 37:1980;70.
17. Webb G.M. Isothermal magnetostatic atmospheres. II. similarity solutions with current proportional to the magnetic potential cubed. Astrophys. J. 327:1988;933.
18. Webb G.M., Zank G.P. Application of the sine-Poisson equation in solar magnetostatics. Solar Phys. 127:1990;229.
19. Zwingmann W. Theoretical study of onset conditions for solar eruptive processes. Solar Phys. 111:1987;309.