Data commit

Task/Euler-method/Go/euler-method.go

@@ -0,0 +1,68 @@
+package main
+
+import (
+    "fmt"
+    "math"
+)
+
+// fdy is a type for function f used in Euler's method.
+type fdy func(float64, float64) float64
+
+// eulerStep computes a single new value using Euler's method.
+// Note that step size h is a parameter, so a variable step size
+// could be used.
+func eulerStep(f fdy, x, y, h float64) float64 {
+    return y + h*f(x, y)
+}
+
+// Definition of cooling rate.  Note that this has general utility and
+// is not specific to use in Euler's method.
+
+// newCoolingRate returns a function that computes cooling rate
+// for a given cooling rate constant k.
+func newCoolingRate(k float64) func(float64) float64 {
+    return func(deltaTemp float64) float64 {
+        return -k * deltaTemp
+    }
+}
+
+// newTempFunc returns a function that computes the analytical solution
+// of cooling rate integrated over time.
+func newTempFunc(k, ambientTemp, initialTemp float64) func(float64) float64 {
+    return func(time float64) float64 {
+        return ambientTemp + (initialTemp-ambientTemp)*math.Exp(-k*time)
+    }
+}
+
+// newCoolingRateDy returns a function of the kind needed for Euler's method.
+// That is, a function representing dy(x, y(x)).
+//
+// Parameters to newCoolingRateDy are cooling constant k and ambient
+// temperature.
+func newCoolingRateDy(k, ambientTemp float64) fdy {
+    crf := newCoolingRate(k)
+    // note that result is dependent only on the object temperature.
+    // there are no additional dependencies on time, so the x parameter
+    // provided by eulerStep is unused.
+    return func(_, objectTemp float64) float64 {
+        return crf(objectTemp - ambientTemp)
+    }
+}
+
+func main() {
+    k := .07
+    tempRoom := 20.
+    tempObject := 100.
+    fcr := newCoolingRateDy(k, tempRoom)
+    analytic := newTempFunc(k, tempRoom, tempObject)
+    for _, deltaTime := range []float64{2, 5, 10} {
+        fmt.Printf("Step size = %.1f\n", deltaTime)
+        fmt.Println(" Time Euler's Analytic")
+        temp := tempObject
+        for time := 0.; time <= 100; time += deltaTime {
+            fmt.Printf("%5.1f %7.3f %7.3f\n", time, temp, analytic(time))
+            temp = eulerStep(fcr, time, temp, deltaTime)
+        }
+        fmt.Println()
+    }
+}