Data commit

Task/Runge-Kutta-method/PowerShell/runge-kutta-method.psh

@@ -0,0 +1,36 @@
+function Runge-Kutta (${function:F}, ${function:y}, $y0, $t0, $dt, $tEnd) {
+    function RK ($tn,$yn)  {
+        $y1 = $dt*(F -t $tn -y $yn)
+        $y2 = $dt*(F -t ($tn + (1/2)*$dt) -y ($yn + (1/2)*$y1))
+        $y3 = $dt*(F -t ($tn + (1/2)*$dt) -y ($yn + (1/2)*$y2))
+        $y4 = $dt*(F -t ($tn + $dt) -y ($yn + $y3))
+        $yn + (1/6)*($y1 + 2*$y2 + 2*$y3 + $y4)
+    }
+    function time ($t0, $dt, $tEnd)  {
+        $end = [MATH]::Floor(($tEnd - $t0)/$dt)
+        foreach ($_ in 0..$end) { $_*$dt + $t0 }
+    }
+    $time, $yn, $t = (time $t0 $dt $tEnd), $y0, 0
+    foreach ($tn in $time) {
+        if($t -eq $tn) {
+            [pscustomobject]@{
+                t = "$tn"
+                y = "$yn"
+                error = "$([MATH]::abs($yn - (y $tn)))"
+            }
+            $t += 1
+        }
+        $yn = RK $tn $yn
+    }
+}
+function F ($t,$y)  {
+    $t * [MATH]::Sqrt($y)
+}
+function y ($t)  {
+    (1/16) * [MATH]::Pow($t*$t + 4,2)
+}
+$y0 = 1
+$t0 = 0
+$dt = 0.1
+$tEnd = 10
+Runge-Kutta  F y $y0 $t0  $dt  $tEnd