Euler method: Difference between revisions
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Step 5 : 100,000 53,800 34,281 26,034 22,549 21,077 20,455 20,192 20,081 20,034 20,014
Step 10 : 100,000 44,000 27,200 22,160 20,648 20,194 20,058 20,017 20,005 20,002 20,000 </pre>
=={{header|Vlang}}==
{{trans|go}}
<lang go>import math
// Fdy is a type for fntion f used in Euler's method.
type Fdy = fn(f64, f64) f64
// euler_step 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.
fn euler_step(f Fdy, x f64, y f64, h f64) f64 {
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.
// new_cooling_rate returns a fntion that computes cooling rate
// for a given cooling rate constant k.
fn new_cooling_rate(k f64) fn(f64) f64 {
return fn[k](delta_temp f64) f64 {
return -k * delta_temp
}
}
// new_temp_func returns a fntion that computes the analytical solution
// of cooling rate integrated over time.
fn new_temp_func(k f64, ambient_temp f64, initial_temp f64) fn(f64) f64 {
return fn[ambient_temp,initial_temp,k](time f64) f64 {
return ambient_temp + (initial_temp-ambient_temp)*math.exp(-k*time)
}
}
// new_cooling_rate_dy returns a fntion of the kind needed for Euler's method.
// That is, a fntion representing dy(x, y(x)).
//
// Parameters to new_cooling_rate_dy are cooling constant k and ambient
// temperature.
fn new_cooling_rate_dy(k f64, ambient_temp f64) Fdy {
// note that result is dependent only on the object temperature.
// there are no additional dependencies on time, so the x parameter
// provided by euler_step is unused.
return fn[k,ambient_temp](_ f64, object_temp f64) f64 {
return new_cooling_rate(k)(object_temp - ambient_temp)
}
}
fn main() {
k := .07
temp_room := 20.0
temp_object := 100.0
fcr := new_cooling_rate_dy(k, temp_room)
analytic := new_temp_func(k, temp_room, temp_object)
for delta_time in [2.0, 5, 10] {
println("Step size = ${delta_time:.1f}")
println(" Time Euler's Analytic")
mut temp := temp_object
for time := 0.0; time <= 100; time += delta_time {
println("${time:5.1f} ${temp:7.3f} ${analytic(time):7.3f}")
temp = euler_step(fcr, time, temp, delta_time)
}
println('')
}
}</lang>
Output, truncated:
<pre>
...
85.0 20.053 20.208
90.0 20.034 20.147
95.0 20.022 20.104
100.0 20.014 20.073
Step size = 10.0
Time Euler's Analytic
0.0 100.000 100.000
10.0 44.000 59.727
20.0 27.200 39.728
30.0 22.160 29.797
40.0 20.648 24.865
50.0 20.194 22.416
60.0 20.058 21.200
70.0 20.017 20.596
80.0 20.005 20.296
90.0 20.002 20.147
100.0 20.000 20.073
</pre>
=={{header|XPL0}}==
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