The approximation solution of a nonlinear parabolic boundary value problem via galerkin finite elements method with crank-Nicolson

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 pre...

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Bibliographic Details
Published in:	Ibn Al-Haitham Journal for Pure and Applied Sciences Vol. 31; no. 3; pp. 126 - 134
Main Authors:	al-Hawwasi, Jamil Amir Ali, Jawad, Marwah Ahmad
Format:	Journal Article
Language:	English
Published:	Baghdad, Iraq University of Baghdad, College of Education for Pure Science / Ibn al-Haitham 13-11-2018 University of Baghdad
Subjects:	nonlinear parabolic boundary value problem, Galerkin finite element methods, Crank-Nicolson
Online Access:	Get full text
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Summary:	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.
ISSN:	1609-4042 2521-3407
DOI:	10.30526/31.3.2002