Alternating direction implicit method for solving parabolic partial differential equations in three dimensions
Joint Authors
al-Ruzbayani, Abd al-Ghafur M.
Yahya, Mahmud H.
Source
al- Rafidain Journal of Computer Sciences and Mathematics
Issue
Vol. 9, Issue 2 (31 Aug. 2012), pp.79-97, 19 p.
Publisher
University of Mosul College of Computer Science and Mathematics
Publication Date
2012-08-31
Country of Publication
Iraq
No. of Pages
19
Main Subjects
Topics
Abstract AR
في هذا البحث تم حل المعادلات التفاضلية الجزئية في ثلاثة أبعاد من نوع القطع المكافئ باستخدام نوعين من طرائق الفروقات المنتهية، طريقة المتجهات المتعاقبة الصريحة (ADE) و طريقة المتجهات المتعاقبة الضمنية (ADI).
بمقارنة النتائج العددية لكل من الطريقتين السابقتين مع نتائج الحل المضبوط لوحظ أن النتائج بطريقة المتجهات المتعاقبة الضمنية (ADI) هو أفضل و أقرب إلى الحل المضبوط من نتائج طريقة المتجهات المتعاقبة الصريحة (ADE).
كما تم دراسة استقرارية كل من الطريقتين السابقتين باستخدام طريقة Neumann- .Von
Abstract EN
In this paper, the parabolic partial differential equations in three-dimensions are solved by two types of finite differences, such as, Alternating Direction Explicit (ADE) method and Alternating Direction Implicit (ADI) method.
By the comparison of the numerical results for the previous two methods with the exact solution, we observe that the results of Alternating Direction Implicit (ADI) method is better and nearest to the exact solution compared with the results of Alternating Direction Explicit (ADE) method.
We also studied the numerical stability of both methods by Von-Neumann Method.
American Psychological Association (APA)
al-Ruzbayani, Abd al-Ghafur M.& Yahya, Mahmud H.. 2012. Alternating direction implicit method for solving parabolic partial differential equations in three dimensions. al- Rafidain Journal of Computer Sciences and Mathematics،Vol. 9, no. 2, pp.79-97.
https://search.emarefa.net/detail/BIM-321898
Modern Language Association (MLA)
al-Ruzbayani, Abd al-Ghafur M.& Yahya, Mahmud H.. Alternating direction implicit method for solving parabolic partial differential equations in three dimensions. al- Rafidain Journal of Computer Sciences and Mathematics Vol. 9, no. 2 (2012), pp.79-97.
https://search.emarefa.net/detail/BIM-321898
American Medical Association (AMA)
al-Ruzbayani, Abd al-Ghafur M.& Yahya, Mahmud H.. Alternating direction implicit method for solving parabolic partial differential equations in three dimensions. al- Rafidain Journal of Computer Sciences and Mathematics. 2012. Vol. 9, no. 2, pp.79-97.
https://search.emarefa.net/detail/BIM-321898
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 96-97
Record ID
BIM-321898