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// Example comparing the formula and numeric approximation for parabolic throw.
//
// Copyright (C) 2020 Juan Marín Noguera
//
// This file is part of Solvned.
//
// Solvned is free software: you can redistribute it and/or modify it under the
// terms of the GNU Lesser General Public License as published by the Free
// Software Foundation, either version 3 of the License, or (at your option) any
// later version.
//
// Solvned is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
// A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
// details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with Solvned. If not, see <https://www.gnu.org/licenses/>.
package main
import (
"fmt"
"math"
"github.com/JwanMan/mned"
"github.com/JwanMan/mned/ivp"
"github.com/JwanMan/mned/method"
)
type methodDescriptor struct {
name string
m mned.Method
}
const step = 0.01
var methods = [3]methodDescriptor{
{name: "Euler", m: method.Euler(step)},
{name: "Modified Euler", m: method.ModifiedEuler(step)},
{name: "RK4", m: method.RK4(step)},
}
func normdiff(p1 []float64, p2 []float64) float64 {
var norm float64 = 0
for i, v := range p1 {
norm += (v - p2[i]) * (v - p2[i])
}
return norm
}
func maxerr(points []mned.Point, sol func(float64) []float64) float64 {
var max float64 = 0
for _, p := range points {
actual := sol(p.Time)
norm := normdiff(actual, p.Value)
if norm > max {
max = norm
}
}
return max
}
func main() {
// Here we test the precision of different methods against the known
// problem of parabolic throw without air resistance. The problem is
// x''(t) = -gj, so x(t) = -g(t^2/2)j + v0*t + hj, thus
// x(t)[1] = 0 when t = (v0[1] + sqrt(v0[1]^2 + 2hg)) / g
var fallen float64
throw := ivp.ParabolicThrow{
Height: 300,
V0: [2]float64{100, 0},
Mass: 1,
Gravity: ivp.EARTH_GRAVITY,
}
problem := throw.ToIVP()
realSolution := func(t float64) []float64 {
return []float64{
throw.V0[0] * t,
throw.Height + throw.V0[1]*t - throw.Gravity*t*t/2,
throw.V0[0],
throw.V0[1] - throw.Gravity*t,
}
}
realEnd := (throw.V0[1] + math.Sqrt(
throw.V0[1]*throw.V0[1]+2*throw.Height*throw.Gravity,
)) / throw.Gravity * throw.V0[0]
for _, method := range methods {
solution := mned.CacheSolve(
method.m, &problem, mned.LinearInterpolator{},
mned.Event{
Cross: func(p *mned.Point) float64 {
return p.Value[1]
},
Tolerance: 0.01,
Action: func(p *mned.Point) bool {
fallen = p.Value[0]
return false
},
})
solution.StepToEnd()
soldiff := maxerr(solution.ForwardPoints(), realSolution)
enddiff := math.Abs(fallen - realEnd)
fmt.Printf("%v: Point diff @ %v, end diff @ %v.\n",
method.name, soldiff, enddiff)
}
}
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