Numerical Solution for Partial Differential Equations (PDE's): The Stability of One Space Dimension Diffusion Equation with Finite Difference Methods - Couverture souple

Mkwizu, Michael

 
9783846582398: Numerical Solution for Partial Differential Equations (PDE's): The Stability of One Space Dimension Diffusion Equation with Finite Difference Methods
Couverture souple
ISBN 10 : 3846582395 ISBN 13 : 9783846582398
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

This book is intended to determine the stability of one space dimension diffusion equation. A Matlab code of finite difference methods with increment of time-space was used in which the behaviour of the errors was observed from the graphs. The explicit scheme was stable with Dirichlet boundary condition when considering space for r less than or equal to 0.5. It was observed that as the gradient alpha of temperature decreases with derivative boundary conditions, the interval of r for the explicit scheme stet stable decreases from the values r less than or equal to 0.5 corresponding to Dirichlet boundary conditions. When the term with coefficient gamma is added to the PDE,explicit scheme becomes stable depending to the value of gamma. The Crank-Nicolson and semi-analytic schemes were stable with both Dirichlet boundary conditions and derivative boundary conditions for all r. It was observed that the Crank-Nicolson scheme was accurate than explicit scheme. The semi-analytic method has only one source of error, the space discretization also it is able to solve for a vector of time simultaneously. But with sufficient small r all three methods were performed well.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

This book is intended to determine the stability of one space dimension diffusion equation. A Matlab code of finite difference methods with increment of time-space was used in which the behaviour of the errors was observed from the graphs. The explicit scheme was stable with Dirichlet boundary condition when considering space for r less than or equal to 0.5. It was observed that as the gradient alpha of temperature decreases with derivative boundary conditions, the interval of r for the explicit scheme stet stable decreases from the values r less than or equal to 0.5 corresponding to Dirichlet boundary conditions. When the term with coefficient gamma is added to the PDE,explicit scheme becomes stable depending to the value of gamma. The Crank-Nicolson and semi-analytic schemes were stable with both Dirichlet boundary conditions and derivative boundary conditions for all r. It was observed that the Crank-Nicolson scheme was accurate than explicit scheme. The semi-analytic method has only one source of error, the space discretization also it is able to solve for a vector of time simultaneously. But with sufficient small r all three methods were performed well.

Biographie de l'auteur

Michael Mkwizu holds MSc.Mathematical Modelling degree of University of Dar es Salaam.He has taught Physics and Mathematics for years in secondary schools in Tanzania. His research area include Numerical analysis. Currently,he is an Assistant Lecturer in the Department of Biometry and Mathematics at Sokoine University of Agriculture.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
3846582395
ISBN 13 
9783846582398
Reliure
Broché
Nombre de pages
68
Coordonnées du fabricant
non disponible
Personne responsable
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