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

• 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
• ISSN: 1609-4042; 2521-3407
• DOI: 10.30526/31.3.2002

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.