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

Michael Mkwizu

ISBN 10: 3846582395 / ISBN 13: 9783846582398

Published by LAP LAMBERT Academic Publishing, 2012

About this Item

Numerical Solution for Partial Differential Equations (PDE's) | The Stability of One Space Dimension Diffusion Equation with Finite Difference Methods | Michael Mkwizu | Taschenbuch | 68 S. | Englisch | 2012 | LAP LAMBERT Academic Publishing | EAN 9783846582398 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu.

Seller Inventory # 106635307

Bibliographic Details

• Title: Numerical Solution for Partial Differential Equations (PDE's) | The Stability of One Space Dimension Diffusion Equation with Finite Difference Methods
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2012
• Language: English
• ISBN 10: 3846582395
• ISBN 13: 9783846582398
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 5D millimeters 220 millimeters width by 150 millimeters height by 5 millimeters depth
• Weight: 119 grams
• Seller catalogs:
  • Bücher

About this title

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.

About the Author

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.