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# Untitled

a guest Sep 5th, 2019 101 Never
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1. nu = 51
2. sig = 0.0011
3. K=23490
4. mu=3.9
5.
6. ### calcul de Emid
7.
8. #fonction pour l'intégrale double
9. f <- function(t,s){
10.   a <- (exp(s)-1)/s
11.   b <- (sig**2*t/6 + sig**2)*exp(-mu*t)*a
12.   c <-  nu*exp(-nu*t)*b
13.   return(c)
14. }
15.
16. #fonction pour l'intégrale simple
17. g <- function(t){
18.   a <- nu*exp(-nu*t)
19.   b <- sig**2*t/3*(1-exp(-mu*t))
20.   return(a*b)
21. }
22.
23.
24. emid <- function(h){
25.
26.   tmin <- h
27.   tmax <- 100
28.   smax <- function(x) mu*x
29.   smin <- 0
30.
31.   I <- integral2(f,tmin,tmax,smin,smax)\$Q
32.
33.   J <- integrate(g,h,100)\$value
34.
35.   a <- (1 - exp(-nu*h)*(nu/(nu+h)))*exp(nu*h)
36.
37.   return(a*(I+J))
38. }
39.
40.
41. #### calcul de E final
42.
43. # fonction pour l'intégrale triple
44. k <- function(t,s,u){
45.   a <- (exp(u)-1)/u
46.   b <- 1/s
47.   c <- nu*exp(-nu*t)*exp(-mu*t)
48.   return(a*b*c)
49. }
50.
51. efin <- function(h){
52.
53.   tmin <- h
54.   tmax <- 100
55.   smax <- function(x) mu*x
56.   smin <- 0
57.   umax <- function(x,y) y
58.   umin <- 0
59.
60.   I <- integral3(k,tmin,tmax,smin,smax,umin,umax)
61.
62.   a <- (1-exp(-mu*h)*mu/(mu+h))
63.   b <- exp(mu*h)/a
64.   J <- nu**2*(nu*h+0.5)
65.
66.   e <- emid(h) + (J/K**2)*b*I
67.   return(e)
68. }
69.
70.
71. #Graphique
72. c <- 0.1 * 1:140
73. d <- lapply(c,efin)
74.
75. plot(c,d,xlab = 'h en secondes',ylab = 'E(h)',main = 'Courbe de E(h)')
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