id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6140	Khalil, Manar; Hashim, Ishak ; Rasheed, Maan; Momani, Shaher	Finite Difference Scheme for One-dimensional Coupled Parabolic System with Blow-up	2025	17	.pdf	application/pdf	5712	374	83	I − 1) where enui = uni − Un i , envi = vni − V n i , uni = u (xi, tn) , vni = v (xi, tn) is the exact solution of problem (1) Suppose that e0ui = 0, e0vi = 0 ∀i = 0, 1, . . Since (1− rn) ≥ 0, it follows that∥∥En+1 u ∥∥ ≤ (1− rn) ∥En u∥+ rn ∥En u∥+ L1kn ∣∣vnj − V n j ∣∣+ ∣∣∣Tn+1/2 ui ∣∣∣∥∥En+1 u ∥∥ ≤ ∥En u∥+ Lk ∥En v ∥+ ∣∣∣Tn+1/2 ui ∣∣∣ ≤ Cn ( k + h2 ) + kLCn ( k + h2 ) + C ( k + h2 ) ≤ (1 + kL)Cn ( k + h2 ) + C ( k + h2 )	cache/ejpam-6140.pdf	txt/ejpam-6140.txt