Taik-cours1_AN3

A. Taik Cours AN3 LST-MI
Implementation numérique
code:
clear all;clc;
syms a b c e x u;
a=input(’donner la valeur de a:’);
b=input(’donner la valeur de b: ’);
c=input(’donner la valeur de c: ’);
e=input(’donner la valeur de e: ’);
dx=input(’entrer le pas de la discretisation: ’);
delta=b*b-4*a*c; m=(b-sqrt(delta))/(2*a); n=1/dx; N=n;
d=zeros(N+1,n+1); t=zeros(N+1,n+1); p=zeros(N+1,n+1);
q=zeros(N+1,n+1); u=12*x; f=diff(u);
u=4-4*x; g=diff(u); y=0:dx:1;
i=1;
for j=1:n+1
d(i,j)=y(i,j);
if(0.25<=d(i,j))
u(i,j)=4-4*d(i,j);
p(i,j)=subs(g,x,d(i,j));
q(i,j)=0;
else
if(d(i,j)==0)
u(i,j)=12*d(i,j);
p(i,j)=subs(f,x,d(i,j));
q(i,j)=0;
end
end
end for i=2:N+1
for j=2:n
d(i,j)=(d(i-1,j-1)+d(i-1,j+1))/(2);
t(i,j)=t(i-1,j-1)+m*(d(i,j)-d(i-1,j-1));
A=[a*m c ; -a*m c];
B=[a*m*p(i-1,j-1)+c*q(i-1,j-1)-e*(t(i,j)-t(i-1,j-1)) ;
-a*m*p(i-1,j+1)+c*q(i-1,j+1)-e*(t(i,j)-t(i-1,j+1))];
V=A\B;
p(i,j)=V(1);
q(i,j)=V(2);
u(i,j)=((p(i,j)+p(i-1,j-1))/2)*(d(i,j)-d(i-1,j-1))
+((q(i,j)+q(i-1,j-1))/2)*(t(i,j)-t(i-1,j-1))+u(i-1,j-1);
end
Département de Mathématiques
FST-Mohammedia, (2008)
44