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The approximation solution of a nonlinear parabolic boundary value problem via galerkin finite elements method with crank-Nicolson
Joint Authors
Jawad, Marwah Ahmad
al-Hawwasi, Jamil Amir Ali
Source
Ibn al-Haitham Journal for Pure and Applied Science
Issue
Vol. 31, Issue 3 (31 Dec. 2018), pp.126-134, 9 p.
Publisher
University of Baghdad College of Education for Pure Science / Ibn al-Haitham
Publication Date
2018-12-31
Country of Publication
Iraq
No. of Pages
9
Main Subjects
Abstract EN
This paper deals with finding the approximation solution of a nonlinear parabolic boundary value problem (NLPBVP) by using the Galekin finite element method (GFEM) in space and Crank Nicolson (CN) scheme in time, the problem then reduces to solve a Galerkin nonlinear algebraic system(GNLAS).
The predictor and the corrector technique (PCT) is applied here to solve the GNLAS, by transforms it to a Galerkin linear algebraic system (GLAS).
This GLAS is solved once using the Cholesky method (CHM) as it appears in the matlab package and once again using the Cholesky reduction order technique (CHROT) which we employ it here to save a massive time.
The results, for CHROT are given by tables and figures and show the efficiency of this method, from other sides we conclude that the both methods are given the same results, but the CHROT is very fast than the CHM.
American Psychological Association (APA)
al-Hawwasi, Jamil Amir Ali& Jawad, Marwah Ahmad. 2018. The approximation solution of a nonlinear parabolic boundary value problem via galerkin finite elements method with crank-Nicolson. Ibn al-Haitham Journal for Pure and Applied Science،Vol. 31, no. 3, pp.126-134.
https://search.emarefa.net/detail/BIM-900681
Modern Language Association (MLA)
al-Hawwasi, Jamil Amir Ali& Jawad, Marwah Ahmad. The approximation solution of a nonlinear parabolic boundary value problem via galerkin finite elements method with crank-Nicolson. Ibn al-Haitham Journal for Pure and Applied Science Vol. 31, no. 3 (2018), pp.126-134.
https://search.emarefa.net/detail/BIM-900681
American Medical Association (AMA)
al-Hawwasi, Jamil Amir Ali& Jawad, Marwah Ahmad. The approximation solution of a nonlinear parabolic boundary value problem via galerkin finite elements method with crank-Nicolson. Ibn al-Haitham Journal for Pure and Applied Science. 2018. Vol. 31, no. 3, pp.126-134.
https://search.emarefa.net/detail/BIM-900681
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 133-134
Record ID
BIM-900681