Programmes Maple (merci de ne rien mettre d'autres)

> lagb:=proc() #on place x0, y0, x1, y1, x2,
y2,.......................,xn, yn.
> local n, p, q, x, i, l, li;
> n:=nargs/2 : p:=0 :q:=1/product(x-args[2*i-1], i=1..n):
> for i from 1 to n do
> l:=q/(x-args[2*i-1]):
> li:=l/subs(x=args[2*i-1],l):
> p:=p+args[2*i]*li:
> od:
> p:=sort(simplify(expand(p))):
> print(p);
> end:

> lagb(1,2,3,4):

Explications (et programmes) sur l'interpolation de lagrange

http://perso-math.univ-mlv.fr/users/pajor.alain/ens/deug/s4mias/interpol1.html
http://perso-math.univ-mlv.fr/users/pajor.alain/ens/deug/s4mias/interpol.txt



Recherge Google

http://www.google.fr/search?hl=fr&q=interpolation+de+lagrange+%28maple%29&btnG=Recherche+Google&meta=

> lag:=proc() #on place x0, y0, x1, y1, x2, y2
> ,.......................,xn, yn.
> local n, p, q, x, i, l, li;
> n:=nargs/2 : p:=0 :q:=product(x-args[2*i-1], i=1..n):
> for i from 1 to n do
> l:=q/(x-args[2*i-1]):
> li:=l/subs(x=args[2*i-1],l):
> p:=p+args[2*i]*li:
> od:
> p:=sort(simplify(expand(p))):
> print(p);
> end:
> lag(575555,5):

5

>
> lagbis:=proc() #on place x0, x1, x2 ,.......................,xn,
> x->f(x) à interpoler en xi, f(xi).
> local n, p, q, x, i, l, li;
> n:=nargs-1 : p:=0 :q:=product(x-args[i], i=1..n): #i désigne ici xi
> for i from 1 to n do
> l:=q/(x-args[i]):
> li:=l/subs(x=args[i],l):
> p:=p+args[nargs](args[i])*li:
> od:
> p:=sort(simplify(expand(p))):
> print (evalf(p));
> end:
> lagbis(3,4,x->x**100):

61 61
.1606938044 10 x - .4820814133 10

>

RK1:=proc(f,a,b,N,Y0)local h,X,Y,i,sol;
> h:=(b-a)/N:
> sol:=NULL:
> X:=a:
> Y:=Y0:
> sol:=sol,[X,Y]:
> for i from 1 to N do
> Y:=Y+h*f(X,Y):
> X:=X+h:
> sol:=sol,[X,Y]:
> od:
> RETURN(sol);
> end:
> f:=(x,y)->exp(x*sin(x));
>

f := (x, y) -> exp(x sin(x))

> RK1(f,0,100,50,1);
>