Solution of the Porous Media Equation by a Compact Finite Difference Method
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-04-06
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time.
In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered.
Therefore, this scheme causes to less accumulation of numerical errors and less use of storage space.
The computed results obtained by this way have been compared with the exact solutions to show the accuracy of the method.
The approximate solutions to the equation have been computed without transforming the equation and without using linearization.
Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy.
This method is seen to be a very good alternative method to some existing techniques for such realistic problems.
American Psychological Association (APA)
Sari, Murat. 2009. Solution of the Porous Media Equation by a Compact Finite Difference Method. Mathematical Problems in Engineering،Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-507499
Modern Language Association (MLA)
Sari, Murat. Solution of the Porous Media Equation by a Compact Finite Difference Method. Mathematical Problems in Engineering No. 2009 (2009), pp.1-13.
https://search.emarefa.net/detail/BIM-507499
American Medical Association (AMA)
Sari, Murat. Solution of the Porous Media Equation by a Compact Finite Difference Method. Mathematical Problems in Engineering. 2009. Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-507499
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507499