Runge-Kutta method: Difference between revisions

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 <lang perl6>sub runge-kutta(&yp, \δt) {
     return -> \t, \y {
-	my @dy =  δt * yp( t       , y );
+	t + δt, y + 6 R/ [+] <1 2 2 1> Z*
+	map {
-	push @dy, δt * yp( t + δt/2, y + @dy[0]/2 );
+	    state $yp = 0;
-	push @dy, δt * yp( t + δt/2, y + @dy[1]/2 );
-	push @dy, δt * yp( t + δt  , y + @dy[2] );
+	    δt* ($yp = yp(t + $_*δt, y + δt*$_*$yp))
-	t + δt, y + 6 R/ [+] <1 2 2 1> Z* @dy;
+	}, <0 1/2 1/2 1>;
     }
 }
 my &RK = runge-kutta { $^t * sqrt($^y) }, .1;
 loop ( my ($t, $y) = (0, 1); $t <= 10; ($t, $y) = RK($t, $y)) {
-    printf "y(%2.0f) = %12f ± %e\n", $t, $y, abs($y - ($t**2 + 4)**2 / 16)
+    printf "y(%2.0f) = %12f ± %e\n", $t, $y, abs($y - ($t**2 + 4)**2 / 16)
     if $t == $t.Int;
+}</lang>
-}
-</lang>
 {{out}}
 <pre>y( 0) =     1.000000 ± 0.000000e+00