Documentation ¶
Overview ¶
Package odeint implements Ordinary Differential Equations integrators. for initial value problems to be solved by explicit methods. The package features methods for the standard library types,
Here you will find several useful examples to get started with this package.
Examples ¶
There are several examples implemented at https://github.com/Daniel-M/odeint/tree/master/examples
Example - Simple harmonic oscillator with float32 ¶
The integrator can be used to integrate the ODE for the harmonic oscillator.
x'' + p*x' + k*x = 0
which can be decomposed as the system,
x' = u u' = -p*u - k*x
If we want to solve the system using float32, we must import the adequate subpackage,
import "github.com/Daniel-M/odeint/float32"
So we begin by defining the system of coupled differential equations
func odesys(x []float32, parameters []float32) []float32 { dxdt := make([]float32, len(x)) dxdt[0] = x[1] dxdt[1] = -parameters[0]*x[0] - parameters[1]*x[1] return dxdt }
declare the state and parameters variables,
state := make([]float32, 2) params := make([]float32, 2)
Putting the inital conditions
state[0] = 0.2 state[1] = 0.8
And the parameters
params[0] = 1.2 * 1.2 params[1] = 0.2
We create an instance of the system,
system := odeint.NewSystem(state, params, odesys)
And an instance of the integrator with Midpoint method,
var integrator odeint.Midpoint
Set the system to the integrator before integrating the system
err := integrator.Set(0.1, *system) if err != nil { panic(err) }
And finally we integrate within a loop
for i := 0; i < int(30.0/integrator.StepSize()); i++ { fmt.Println(float32(i)*integrator.StepSize(), state) state, err = integrator.Step() if err != nil { panic(err) } }
The code above will print the data columns to the standard output. To write to a file you could create a file with
os.Create
and write to it with
fmt.Fprintf(w,...)
where w implements the interface
io.Writter
Example with complex64 ¶
If we want to solve the system using complex64, we must import the adequate subpackage,
import "github.com/Daniel-M/odeint/complex64"
So we begin by defining the system of coupled differential equations, for instance,
func odesys(x []complex64, parameters []complex64) []complex64 { dxdt := make([]complex64, len(x)) dxdt[0] = -1i * x[0] * x[0] * x[1] dxdt[1] = 1i * x[1] return dxdt }
declare the state and parameters variables,
state := make([]complex64, 2) params := make([]complex64, 2)
Putting the inital conditions
state[0] = 1 / 2.1 state[1] = 0.8
And the parameters
params[0] = 2.0 params[1] = 0.0
We create an instance of the system,
system := odeint.NewSystem(state, params, odesys)
And an instance of the integrator with Midpoint method,
var integrator odeint.Midpoint
Set the system to the integrator before integrating the system
err := integrator.Set(2*math.Pi/500, *system) if err != nil { panic(err) }
And finally we integrate within a loop
for i := 0; i <= int(2*math.Pi/real(integrator.StepSize()))+1; i++ { fmt.Println(float64(i)*real(integrator.StepSize()), state) state, err = integrator.Step() if err != nil { panic(err) } }
The code above will print the data columns to the standard output. To write to a file you could create a file with
os.Create
and write to it with
fmt.Fprintf(w,...)
where w implements the interface
io.Writter
There are more examples at the examples path
License ¶
This code is licensed under MIT license that can be found in the LICENSE file as,
MIT License Copyright (c) 2017-2018 Daniel Mejía Raigosa Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
And at the begining of the source code files as the fragment,
Copyright 2017-2018 Daniel Mejía Raigosa. All rights reserved. Use of this source code is governed by a MIT license that can be found in the LICENSE file.