Calcul de la Dynamique de Verhulst
(R+1)X-R(XX)
Avec R=3 :
IBM ES9000 :
(R+1)X-R(XX) (R+1)X-(RX)X ((R+1)-(RX))X RX+(1-(RX))X X+R(X-(XX))
X(00) = 0.500000 0.500000 0.500000 0.500000 0.500000
X(10) = 0.384631 0.384631 0.384631 0.384631 0.384631
X(20) = 0.418895 0.418895 0.418895 0.418895 0.418895
X(30) = 0.046399 0.046399 0.046399 0.046399 0.046399
X(40) = 0.320185 0.320183 0.320188 0.320182 0.320189
X(50) = 0.063406 0.064521 0.061895 0.064941 0.061244
X(60) = 1.040381 0.846041 0.529794 1.319900 1.214070
X(70) = 0.004104 1.199452 0.873553 0.573637 0.000009
X(80) = 0.108044 0.121414 1.260726 0.395871 0.280590
X(90) = 0.096374 0.089244 0.582157 0.344503 1.023735
IBM RS6000 :
(R+1)X-R(XX) (R+1)X-(RX)X ((R+1)-(RX))X RX+(1-(RX))X X+R(X-(XX))
X(00) = 0.500000 0.500000 0.500000 0.500000 0.500000
X(10) = 0.384631 0.384631 0.384631 0.384631 0.384631
X(20) = 0.418895 0.418895 0.418895 0.418895 0.418895
X(30) = 0.046399 0.046399 0.046399 0.046399 0.046399
X(40) = 0.320177 0.320184 0.320188 0.320190 0.320189
X(50) = 0.067567 0.063747 0.061859 0.060822 0.061486
X(60) = 0.001145 0.271115 0.616781 0.298613 1.307350
X(70) = 1.296775 1.328462 0.486629 0.938605 1.054669
X(80) = 0.553038 0.817163 1.277151 1.325437 0.617058
X(90) = 0.094852 0.154184 1.174162 0.148151 0.237355
Power-Challenge M Silicon Graphics (R8000, IRIX 6.2, cc 7.0) :
option '-O2' option '-O3'
X(00) = 0.500000 0.500000
X(10) = 0.384631 0.384631
X(20) = 0.418895 0.418895
X(30) = 0.046399 0.046399
X(40) = 0.320184 0.320188
X(50) = 0.063747 0.061859
X(60) = 0.271115 0.616781
X(70) = 1.328462 0.486629
X(80) = 0.817163 1.277151
O200 Silicon Graphics (R10000, IRIX 6.5.5m, cc 7.2.1) :
option '-O2' option '-O3'
X(00) = 0.500000 0.500000
X(10) = 0.384631 0.384631
X(20) = 0.418895 0.418895
X(30) = 0.046399 0.046399
X(40) = 0.320184 0.320192
X(50) = 0.063747 0.059988
X(60) = 0.271115 1.000531
X(70) = 1.328462 1.329692
X(80) = 0.817163 0.021952
(calculs effectués en double précision, c'est-à-dire sur 64 bits).
O200 Silicon Graphics (processeur R10000, IRIX 6.5.5m, Java) :
(R+1)X-R(XX) (R+1)X-(RX)X ((R+1)-(RX))X RX+(1-(RX))X X+R(X-(XX))
X(0000) = 0.5 0.5 0.5 0.5 0.5
X(0500) = 1.288736212247168 0.007057813075738616 1.2767485100695732 1.246534177059494 0.03910723014701789
X(1000) = 1.3327294162589722 0.916560711983132 1.207710752523091 0.27770146115891703 0.26663342726567785
X(1500) = 1.1448646685382955 0.4481000759915065 0.3102077001456977 0.015374092695375374 0.9841637252962943
X(2000) = 1.0548628914440754 0.896126931497168 0.6851138190159249 0.009229885271816535 0.3860923315999224
X(2500) = 1.292802584458599 0.06063433547953646 1.174118726001978 0.6922411856638806 0.020878761210912034
X(3000) = 1.0497821908090537 0.0219606878364607 1.3287403237319588 0.11354602472378028 0.13270749449424302
X(3500) = 0.8115039383609847 1.3213031319440816 0.6545151597367076 0.5760786099237328 1.324039473116061
X(4000) = 0.04922223042798102 1.3203298564077224 0.09243804931690679 0.9496284087750142 1.316597313359563
X(4500) = 0.4745896653599724 0.32865616721789603 0.018965010461877246 0.25384661313701296 0.18512853535354462
PC (processeur Pentium II, LINUX Mandrake 7.0, Java) :
(R+1)X-R(XX) (R+1)X-(RX)X ((R+1)-(RX))X RX+(1-(RX))X X+R(X-(XX))
X(0000) = 0.5 0.5 0.5 0.5 0.5
X(0500) = 1.2887362122471679 0.00705781307573862 1.2767485100695732 1.2465341770675666 0.03910723014701789
X(1000) = 1.3327294162589722 0.91656071198313205 1.207710752523091 0.6676224369769922 0.26663342726567785
X(1500) = 1.1448646685382955 0.44810007599150647 0.31020770014569771 0.41049165176544455 0.98416372529629426
X(2000) = 1.0548628914440754 0.89612693149716804 0.68511381901592494 1.0026346845706315 0.3860923315999224
X(2500) = 1.3328681064703032 0.06063433547953646 1.1741187260019781 0.0154001182074282 0.02087876121091203
X(3000) = 1.2956769824648844 0.0219606878364607 1.3287403237319588 0.50504896336548377 0.13270749449424302
X(3500) = 0.19193027175727995 0.37986077053509781 0.6545151597367076 0.38299434265835819 1.324039473116061
X(4000) = 1.2491385720940165 0.96017143401896088 0.09243804931690679 0.6565274346305322 1.316597313359563
X(4500) = 0.00644889182443986 1.3185465795235045 0.01896501046187725 0.94966313327336349 0.18512853535354462
Les valeurs correctes sont (avec 16 décimales) :
X(00) = 0.5000000000000000
X(10) = 0.3846309658187955
X(20) = 0.4188950250152601
X(30) = 0.0463994768425783
X(40) = 0.3201870617215119
X(50) = 0.0622361944358458
X(60) = 0.0049027225204761
X(70) = 0.5530823826833586
X(80) = 0.1196398066817574
X(90) = 0.3109290853617026
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
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