CCINP Informatique Commune PC 2015

\# II.B.2.j.(iv)
T_tous_k[ : , 0]=T0
\# II.B.2.j. (v)
T_tous_k[0,1]=r*Tint+(1-2*r)*T_tous_k[0,0]+r*T_tous_k[1,0]
T_tous_k[N-1,1] $=r^{*}$ T_tous_k[N-2,0]+(1-2*r)*T_tous_k[N-1,0]+r*Text
for i in range ( $2, \mathrm{~N}$ ) :
    T_tous_k[i-1,1]=r*T_tous_k[i-2,0]+(1-2*r)*T_tous_k[i-1,0]+r*T_tous_k[i,0]
\# II.B.2.j. (vi)
def calc_norme(V):
    $\mathrm{N}=$ len (V)
    $s=0$
for
        $i$ in $\operatorname{range}(N):$
$s+=V[i]^{* * 2}$
    return sqrt(s)
\# II.B.2.j.(vii)
k=1
while calc_norm( $\mathrm{T}[:, \mathrm{k}]-\mathrm{T}[:, \mathrm{k}-1])>=10^{* *}(-2)$ and $\mathrm{k}<$ ItMax-1:
    k+=1
    T_tous_k[0,k]=r*Tint+(1-2*r)*T_tous_k[0,k-1] +r*T_tous_k[1,k-1]
    T_tous_k[N-1,k]=r*T_tous_k[N-2, k-1]+(1-2*r)*T_tous_k[N-1, k-1]+r*Text
    for i in range $(2, N)$ :
[i,k-1]
\# II.B.2.j.(viii)
nbIter=k
return nbIter, T_tous_k
\# II.B.3.a. l'équation (1) donne
\# alpha * ( T^\{k+1\}_i - T^k_i )/( Delta t ) = ( T^\{k+1\}_\{i+1\} + T^\{k+1\}_\{i-1\} -
2. $\mathrm{T} \wedge\{\mathrm{k}+1\} \_$i )/( Delta $\mathrm{x}^{\wedge} 2$ )
\# II.B.3.b.on a donc
\# T^k_i=-r. T^\{k+1\}_\{i-1\}+(1+2r). T^\{k+1\}_i-r.t^\{k+1\}_\{i+1\}
\# toujours avec r=(Delta t / (alpha*Delta x^2))
\# II.B.3.c.
\# M est tridiagonale: sur la diagonale principale tous les coefficients valent 1
$+2 r$
\# sur la diagonale supérieure tous les coefficients valent $r$
\# sur la diagonale inférieure tous les coefficients valent $r$
\# v=[Tint,0,.....,0,Text2]
\# II.B.3.d.
def CalcTkp1(M,d):
    N=1en(d)
    cprime=[ 0 for k in range( N )
    cprime[0]=M[0,1]/float(M[0,0]) \# Python 2.7
    for 1 range(1, N-1):
    dprime=
    dprime[0]=float(d[0])/M[0,0] \# Python 2.7
    dprimplon 2.7
    for i in range( $1, \mathrm{~N}$ ):
\# dprime[i]=float(d[i]-M[i,i-1]*dprime[i-1])/(M[i,i]-M[i,i-1]*cprime[i-1])
\# Python 2.7
    - [ or k in range(N) ]
    u[-1]=dprime[-1]
    for $i$ in range( $N-2,-1,-1$ ):