TY - JOUR
AU - Al-Hawasy, Jamil Amir
AU - Jawad, Marwa Ahmed
PY - 2018/11/13
Y2 - 2022/10/07
TI - The Approximation Solution of a Nonlinear Parabolic Boundary Value Problem Via Galerkin Finite Elements Method with Crank-Nicolson
JF - Ibn AL-Haitham Journal For Pure and Applied Sciences
JA - IHJPAS
VL - 31
IS - 3
SE - mathematics
DO - 10.30526/31.3.2002
UR - https://jih.uobaghdad.edu.iq/index.php/j/article/view/2002
SP - 126-134
AB - <p><strong> </strong>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 reduce 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 appear 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.</p><p> </p>
ER -