id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3411	Youssouf, Minoungou; Moussa, Bagayogo; Pare, Youssouf	General Solution of Linear Partial Differential Equations Modeling Homogeneous diffusion-convection-reaction Problems with Cauchy Initial Condition	2019	14	.pdf	application/pdf	3987	196	84	[2, 4] (PSBA) :  uk0 (t, x) = sinωx ukn+1 (t, x) = ε ∫ t 0 ∂2ukn (s, x) ∂x2 ds, n ≥ 0 (9) Let us calculate the following terms: uk1 (t, x) , uk2 (t, x) , uk3 (t, x) , ... uk0 (t, x) = sinωx uk1 (t, x) = −εω2t sinωx uk2 (t, x) = ( εω2t )2 2! We obtain the following algorithm : (PSBA) :  uk0 (t, x) = cosαx ukn+1 (t, x) = λ ∫ t 0 ∂ukn (s, x) ∂x ds, n ≥ 0 (14) Let us calculate the following terms: uk1 (t, x) , uk2 (t, x) , uk3 (t, x) , ...  uk0 (t, x) = cosαx uk1 (t, x) = −tαλ sinαx uk2 (t, x) = −(tαλ)2 2! cosαx uk3 (t, x) = (αλt)3 3! sinαx uk4 (t, x) = (αλt)4 4! cosαx uk5 (t, x) = −(αλt)5 5! sinαx uk6 (t, x) = −(αλt)6 6! cosαx ... uk2n (t, x) = (−1)n (αλt)2n (2n)! cosαx ; n ≥ 0 uk2n+1 (t, x) = − (−1) n (αλt)2n+1 (2n+ 1)! sinαx ; n ≥ 0 Then Y. Minoungou, M. Bagayogo, Y. Paré / Eur.	cache/ejpam-3411.pdf	txt/ejpam-3411.txt