• Chebyshev spectral collocation...

Result: Chebyshev spectral collocation methods for nonlinear isothermal magnetostatic atmospheres

Title:
Chebyshev spectral collocation methods for nonlinear isothermal magnetostatic atmospheres
Authors:
KHATER, A. H, SHAMARDAN, A. B, CALLEBAUT, D. K, IBRAHIM, R. S
Source:
Proceedings of the 8th International Congress on Computational and Applied Mathematics, (ICCAM-98): Leuven, Belgium, 27 July-1 August 1998Journal of computational and applied mathematics. 115(1-2):309-329
Publisher Information:
Amsterdam: Elsevier, 2000.
Publication Year:
2000
Physical Description:
print, 19 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations aux dérivées partielles, problèmes aux valeurs limites, Partial differential equations, boundary value problems, Physique, Physics, Generalites, General, Relativité générale et gravitation, General relativity and gravitation, Systèmes autogravitants; milieux continus et champs classiques en espace-temps courbe, Self-graviting systems; continuous media and classical fields in curved spacetime, Espace-temps d'einstein-maxwell, espace-temps avec fluides, rayonnement ou champs classiques, Einstein-maxwell spacetimes, spacetimes with fluids, radiation or classical fields, Condition aux limites, Boundary condition, Condiciones límites, Equation Liouville, Liouville equation, Ecuación Liouville, Equation Maxwell, Maxwell equation, Ecuación Maxwell, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation elliptique, Elliptic equation, Ecuación elíptica, Equation non linéaire, Non linear equation, Ecuación no lineal, Equation équilibre, Equilibrium equation, Ecuación equilibrio, Erreur troncature, Truncation error, Error truncamiento, Magnétostatique, Magnetostatics, Méthode collocation, Collocation method, Método colocación, Méthode différence finie, Finite difference method, Método diferencia finita, Méthode spectrale, Spectral method, Método espectral, Polynôme Tchebychev, Tchebychev polynomial, Polinomio Tchebychev, Problème valeur limite, Boundary value problem, Problema valor limite, Atmosphère magnétostatique isothermal, Isothermal magnetostatic atmosphere, Matrice méthode El-gendi, Matrix of El-gendi method, Modèle équation Sinh Poisson, Sinh Poisson equation model, Méthode spectrale Tchebychev, Tchebychev spectral method
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Mathematics Department, Faculty of Science, Cairo University, Beni-Suef, Egypt
Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt
Physics Department, U.I.A., University of Antwerp, 2610 Antwerp, Belgium
ISSN:
0377-0427
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=1298212
Rights:
Copyright 2000 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.1298212
Database:
PASCAL Archive

Further Information

The equations of magnetohydrodynamic (MHD) equilibria for a plasma in gravitational field are investigated. For equilibria with one ignorable spatial coordinate, the MHD equations are reduced to a single nonlinear elliptic equation (NLPDE) for the magnetic flux u, known as the Grad-Shafranov equation. The Chebyshev spectral collocation methods (CSCMs) are described and applied to obtain numerical solutions for nonlinear boundary value problems modelling two classes of isothermal magnetostatic atmospheres, in which the current density J is proportional to the exponential of the magnetic flux and moreover falls off exponentially with distance vertical to the base, with an e-folding distance equal to the gravitational scale height, for the first class and proportional to the sinh(u) for the second class. The accuracy and efficiency of this Chebyshev approach are compared favorably with those of the standard finite-difference methods.