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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 60 "Autour de la methode de
 Newton-Cotes d'integration numerique" }{MPLTEXT 1 0 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 33 "Integrat
ion par sommes de Riemann" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 
"riemann := proc(f,a,b,n)\n  local h,k;\n  h := (b-a)/(n-1);\n  RETURN
(h*sum(f(a+k*h),k=0..n-2));\nend;\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "f := x->sin(1/x);\nevalf(riemann(f,0.01,1,10^5)-int(x
^2,x=0.01..1));" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT 258 34 "Integration par sommes de trapezes" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "trapeze := proc(f,a,b,n)\n  local \+
h;\n  h := (b-a)/(n-1);\n  RETURN(h/2*sum(f(a+k*h)+f(a+(k+1)*h),k=0..n
-2));\nend; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 38 "Method
e de Newton Cotes (premier tour)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 149 "NCloc1:= proc(f,a,b,l)\n  local h,X;\n  h := (b-a)/(l-1);  \n
  X := map(t -> a+t*h, [seq(k,k=0..l-1)]);\n  RETURN(int(interp(X,map(
f,X),x),x=a..b));\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 
"NC1 := proc(f,a,b,n,l)\n  local h;  \n  h := (b-a)/(n-1);\n  RETURN(s
um(NCloc1(f,a+k*h,a+(k+1)*h,l),k=0..n-2));\nend;\n" }}}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 36 "Methodede Newt
on Cotes (second tour)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 285 "c
oeffNC := proc(l)\n  local res,j,X,k,Xt,t;\n  res := vector(l+1);\n  f
or j from 0 to l do\n    X := 1;  \n    for k from 0 to l do\n      if
 not k = j then\n        X := X*(l*t-k)/(j-k);\n      fi;\n    od;\n  \+
  Xt := t-> X;\n    res[j+1] := int(Xt(t),t=0..1);\n  od;\n  RETURN(ev
alm(res));\nend;  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "coeff
NC(4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "NCloc2 := proc(f
,a,b,l)\n  local coeff,h,X;\n  coeff := coeffNC(l-1);\n  h := (b-a)/(l
-1);  \n  X := map(t -> a+t*h, [seq(k,k=0..l-1)]);\n  RETURN(sum(coeff
[i]*f(X[i]),i=1..l)*(b-a));\nend;\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 114 "NC2 := proc(f,a,b,n,l)\n  local h;  \n  h := (b-a)/(
n-1);\n  RETURN(sum(NCloc2(f,a+k*h,a+(k+1)*h,l),k=0..n-2));\nend;\n" }
}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 
23 "Mini-methode de Romberg" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 200 "romberg := proc(f,a,b,n,m)\n  local T,i,j;\n  for \+
j from 0 to m do T[j] := trapeze(f,a,b,2^j*n); od;\n  for i to m do\n \+
   for j from 0 to m-i do T[j] := (4^i*T[j+1]-T[j])/(4^i-1); od;\n  od
;\n  T[0];\nend;\n" }}}}}{MARK "5" 0 }{VIEWOPTS 1 1 0 2 1 1805 }