Numerical methods for second order parabolic partial differential equations / Zoulikha Zaidi ep Otmani (1986)

Public ISBD Titre : Numerical methods for second order parabolic partial differential equations Type de document : texte imprimé Auteurs : Zoulikha Zaidi ep Otmani, Auteur ; E.H. Twizell, Directeur de thèse Editeur : London : [s.n.] Année de publication : 1986 Importance : 172 f. Présentation : ill. Format : 30 cm. Note générale : Master Thesis : Mathematics : The university of West London : 1986 Bibliogr. f. 170 - 172 Langues : Anglais (eng) Mots-clés : Numerical Methods Parabolic partial Differential equations Index. décimale : Ms01786 Résumé : The thesis develops a number of numerical methods for solving first order ordinary differential equations. These ordinary differential equations arise when secind order difference operators are used to replace the space derivatives of second order parabolic partial differential equations in one and two space variables. Our main concern in this thesis is not to improve the accuracy with respect to the space discretization process, but to explore the possibility of improving the accuracy with respect to the temporal discretization, achieving up to fourth order accuracy. Higher accuracy could of course be achieved when replacing the exponential function by its higher pade approximants but then the solution would be expensive. It is shown that I0-stable methods are to be preferred to A0-stable schemes when high frequency components in the numerical solution are expected. Emphasis is placed throughout on the cost of implementing each method by counting the number of arithmetic operations and CPU time to evaluate the solution at a certain time, using model problems from the literature. Numerical methods for second order parabolic partial differential equations [texte imprimé] / Zoulikha Zaidi ep Otmani, Auteur ; E.H. Twizell, Directeur de thèse . - London : [s.n.], 1986 . - 172 f. : ill. ; 30 cm. Master Thesis : Mathematics : The university of West London : 1986 Bibliogr. f. 170 - 172 Langues : Anglais (eng) Mots-clés : Numerical Methods Parabolic partial Differential equations Index. décimale : Ms01786 Résumé : The thesis develops a number of numerical methods for solving first order ordinary differential equations. These ordinary differential equations arise when secind order difference operators are used to replace the space derivatives of second order parabolic partial differential equations in one and two space variables. Our main concern in this thesis is not to improve the accuracy with respect to the space discretization process, but to explore the possibility of improving the accuracy with respect to the temporal discretization, achieving up to fourth order accuracy. Higher accuracy could of course be achieved when replacing the exponential function by its higher pade approximants but then the solution would be expensive. It is shown that I0-stable methods are to be preferred to A0-stable schemes when high frequency components in the numerical solution are expected. Emphasis is placed throughout on the cost of implementing each method by counting the number of arithmetic operations and CPU time to evaluate the solution at a certain time, using model problems from the literature.

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Code-barres	Cote	Support	Localisation	Section	Disponibilité	Spécialité	Etat_Exemplaire
Ms01786	Ms01786	Papier	Bibliothèque centrale	Mémoire de Master	Disponible