id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2618	Ali Al-Hawasy, Jamil A.; Mansour, Nuha Farhan	The Galerkin-Implicit Methods for Solving Nonlinear Hyperbolic Boundary Value Problem	2021	10	.pdf	application/pdf	4773	220	82	× 𝐼 , then the NLHYPVP is given by: 𝑤𝑡𝑡 − Δ𝑤 + 𝑤 = ℎ(�⃗�, 𝑡, 𝑤), in 𝜑 (1) 𝑤(�⃗�, 0) = 𝑤0 (�⃗�), in 𝜓 (2) 𝑤𝑡(�⃗�, 0) = 𝑤1 (�⃗�), in 𝜓 (3) 𝑤(�⃗�, 𝑡) = 0 , on Σ (4) where 𝑤 = 𝑤(�⃗�, 𝑡) ∈ 𝐻0 2(𝜓), , Δ𝑤 = ∑ 𝜕2𝑤 𝜕𝑥𝑖 2 2 𝑖=1 and ℎ ∈ 𝐿2(𝜓) is a given function. 𝐼 , 𝜓 = (0,1) × (0,1), 𝐼 = [0,1] 𝑤(�⃗�, 0) = 𝑥𝑦(1 − 𝑥)(1 − 𝑦), in 𝜓 𝑤𝑡(�⃗�, 0) = 𝑤1 (�⃗�) , in 𝜓 𝑤(�⃗�, 𝑡) = 0 , on ∑ = 𝜕𝜓	cache/iajs-2618.pdf	txt/iajs-2618.txt