id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6007	Megahed, Abd El-Monem; M. Kamel, Nesreen ; M. Hanafy, I. ; A. Omar, Nora 	A Numerical Solution for Nash Differential Games Based on the Runge Kutta 4th-order Method	2025	22	.pdf	application/pdf	6390	344	80	For n = 0, x1 − x0 = h 6 Φ1(xn, λ1,n, λ2,n, t), |x1 − x0| = ∣∣∣∣h6Φ1(xn, λ1,n, λ2,n, t) ∣∣∣∣ , |x1 − x0| ≤ h 6 M1. = h [ λ1(t1 + K2λ1 2 )2 P1 (1− (x1 + h 2 )) − λ1(t1 + K2λ1 2 )λ2(t1 + K2λ1 2 ) P2 (x1 + h 2 )− ϕ1 ] , K4λ1 = hFλ1 (x1 + h, t1 +K3x) = h [ λ1(t1 +K3λ1) 2 P1 (1− (x1 + h)) − λ1(t1 +K3λ1)λ2(t1 +K3λ1) P2 (x1 + h)− ϕ1 ] . (45) λ1,2 = −h2ϕ1 + h6 6 [ (ϕ1) 2 P1 ( (1− x0) + 4(1− x0 − h 2 ) + (1− x0 − h) ) − ϕ1ϕ2 P2 ( x0 + 4(x0 + h 2 ) + (x0 + h) )] + ϕ1h 2 (46) A. A. Megahed et al. / Eur.	cache/ejpam-6007.pdf	txt/ejpam-6007.txt