Proceedings Volume 2010 (format .pdf) - SimpBTH

with X1 [ a,b]such that M ( θ )( )1X = n 1X − −na ⎡+ ⎣M X − nα ⎤ ⎦ , a ≠ 0 , (13)∈ arbitrarily chosen. Then, under suitable conditions, Xn⎯⎯⎯→ θn→∞= α .By Newton-Raphson method, we consider iterative relation:1X = n 1X − −na ⎡+ n ⎣M ( Xn ) − α ⎤ ⎦ , (14)where:'⎧ a1 , M ( Xn ) < a1⎪ ''an = ⎨M ( Xn ),a1 ≤ M ( Xn ) ≤ a2, (15)⎪⎩ a2 , M ( Xn ) > a2a1and a 2are constants such that 0 < a1 < a2< ∞ .Though this method involves thecomputation of the derivative of M at each stage of iteration, the eventual rate ofconvergence is improved.The problem of existence of the solution and its uniqueness is solved by Ostrowsky[4]; this implies a result for the problem under consideration.3. RESULTS AND DISCUSSIONSeveral grapevines were taken into study and each 5 days the growingprocess of the main shoots was registered after applying only Atonik in case ofsome plants and only Ronilan in case of the others.We applied the previous theory and the following results were obtained:Atonikdosage(mg / l)Table 1- The observational data for 5 experimentsRonilan Treated by Treated bydosage Atonik Ronilan(mg / l) (growth -cm) (growth -cm)X11= 5 X12= 4,3 Y11= 5, 2 Y12= 5,4X21= 5,3 X22= 4,5 Y21= 5,8 Y22= 6,2X31= 5,6 X32= 4,7 Y31= 7,3 Y31= 7,5X31= 5,7 X32= 4,8 Y31= 7,5 Y31= 7,5X31= 5,8 X32= 4,9 Y31= 7,6 Y31= 7,8YnY1= 5,3Y2= 6Y3= 7,4Y3= 7,5Y3= 7,7331