id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2002	Al-Hawasy, Jamil Amir; Jawad, Marwa Ahmed	The Approximation Solution of a Nonlinear Parabolic Boundary Value Problem Via Galerkin Finite Elements Method with Crank-Nicolson	2018	9	.pdf	application/pdf	3863	148	73	I (2) and the initial condition (i.c) 𝑢 �⃗�, 0 𝑢 �⃗� , in W (3) where 𝑢 𝑢 �⃗�, 𝑡 , ∆𝑢 ∑ is the Laplace operator and 𝐻 ∈ 𝐶 𝑊 . Hence the corrector equation described as follows: 𝑢 𝑢 , 𝜉 ∆𝑡 𝛻𝑢 𝛻𝑢 , 𝛻𝜉 ∆𝑡 𝐻 𝑢 𝑢 , 𝜉 (12) where 𝑢 ∶ 𝑢 is the predictor solution at the iteration 𝑙 1, 𝑢 ∶ 𝑢 is its corresponding corrector solution at the iteration 𝑙 and 𝑢 𝑢 is the known corrector solution for the previous step j, i.e. (12) can be written as : 𝑢 𝑞 𝑢 (13)	cache/iajs-2002.pdf	txt/iajs-2002.txt