Terminaison de la méthode des différences finies, optimisation de la …

…méthode de Tir
Rowin · Apr 10, 2013 · 35a6bea · 35a6bea
1 parent 6a25da5
commit 35a6bea
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Showing 9 changed files with 24 additions and 12 deletions.
diff --git a/Cramer.mn b/Cramer.mn
diff --git a/Cramer.mu b/Cramer.mu
@@ -2,11 +2,12 @@ Cramer := hold(proc(A, l)
   name Cramer;
   local detA, k, n, solutions;
 begin
-  detA := linalg::det(A); 
+  detA := float(numeric::det(A)); 
   n := sqrt(nops(A)); 
   solutions := []; 
   for k from 1 to n do 
-    solutions := [op(solutions), linalg::det(linalg::setCol(A, k, l))/detA]
+    solutions := [op(solutions), float(numeric::det(linalg::setCol(A, k, l))/de\
+tA)]
   end_for; 
   return(solutions)
 end_proc):

diff --git a/Differenciation.mn b/Differenciation.mn
diff --git a/Differenciation.mu b/Differenciation.mu
@@ -1,6 +1,6 @@
 Differenciation := hold(proc(A, B, C, D, x0, x1, y0, y1, r, variable)
   name Differenciation;
-  local pas, i, k, listeA, listeD, matA;
+  local pas, i, k, listeA, listeD, matA, points, solution;
 begin
   pas := (x1 - x0)/(r + 1); 
   A := fp::unapply(A, variable); 
@@ -15,20 +15,27 @@ begin
   k := 0; 
   for i from x0 + pas to x1 - pas step pas do 
     k := k + 1; 
-    listeA := [op(listeA), [0*j $ j = 1..k - 1, a(i), b(i), c(i), 0*j $ j = k +\
- 3..r]]; 
+    listeA := [op(listeA), [0*j $ j = 1..k - 1, float(a(i)), float(b(i)), float\
+(c(i)), 0*j $ j = k + 3..r]]; 
     if i = x0 + pas then 
-      listeD := [op(listeD), D(i) - a(x0)*y0]
+      listeD := [op(listeD), float(D(i) - a(x0)*y0)]
     else 
       if i = x1 - pas then 
-        listeD := [op(listeD), D(i) - c(i)*y1]
+        listeD := [op(listeD), float(D(i) - c(i)*y1)]
       else 
-        listeD := [op(listeD), D(i)]
+        listeD := [op(listeD), float(D(i))]
       end_if
     end_if
   end_for; 
   matA := linalg::delCol(linalg::delCol(matrix(listeA), r + 2), 1); 
   matD := matrix(listeD); 
-  return(matA, matD)
+  solution := Cramer(matA, matD); 
+  t := 0; 
+  points := []; 
+  for i from x0 + pas to x1 - pas step pas do 
+    t := t + 1; 
+    points := [op(points), [i, solution[t]]]
+  end_for; 
+  return(points)
 end_proc):
 
diff --git a/Reso.mn b/Reso.mn
diff --git a/Reso.mu b/Reso.mu
@@ -0,0 +1,2 @@
+delete Reso:
+
diff --git a/Tir.mn b/Tir.mn
diff --git a/Tir.mu b/Tir.mu
@@ -37,6 +37,7 @@ begin
     b := b + hb
   end_while; 
   fab := RK(f, g, x0, x1, y0, (a + b)/2, 100)[-1][2]; 
+  w := 1; 
   repeat 
     if y1 < fab then 
       a := float((a + b)/2)
@@ -45,13 +46,14 @@ begin
         b := float((a + b)/2)
       end_if
     end_if; 
-    fab := RK(f, g, x0, x1, y0, (a + b)/2, 100)[-1][2]; 
+    fab := RK(f, g, x0, x1, y0, (a + b)/2, floor(exp(floor(p/w) + 10)))[-1][2];\
+
     w := abs(fab - y1)/abs(y1); 
-    print(w)
+    print(w, floor(exp(floor(p/w) + 10)))
   until w <= p end_repeat; 
   fonction := []; 
   derivee := []; 
-  points := RK(f, g, x0, x1, y0, (a + b)/2, 100); 
+  points := RK(f, g, x0, x1, y0, (a + b)/2, floor(exp(11))); 
   for i from 1 to nops(points) do 
     fonction := [op(fonction), [points[i][1], points[i][2]]]; 
     derivee := [op(derivee), [points[i][1], points[i][3]]]

diff --git a/main.mn b/main.mn