odeint

README

odeint

Description

Go package with ordinary differential equations solvers for initial value problems to be solved by explicit methods. The package features methods for float32 float64 complex64 and complex128 types. The methods implemented so far are,

• Euler
• Mid point
• Runge-Kutta 4

The package is easily extensible to provide other methods.

The docs,

The API is pretty consistent, and you'll get it easily,

• Getting started

Type specific docs,

• GoDoc documentation for float32
• GoDoc documentation for float64
• GoDoc documentation for complex64
• GoDoc documentation for complex128

Usage

Import the type you intend to use. For the recommended float64 just type

import "github.com/Daniel-M/odeint/float64"   

and you are ready to use methods. The stepper used (euler, mid point or Runge-Kutta-4) can be changed easily.

To get a feeling of the usage check the files under examples/brusselator. You will see that to change the method used you just need to change the integrator used (line 38 of examples/brusselator/rk4 source code).

FAQ

A subpackage for each numeric type?

You might be thinking, why does this guy have a subpackage for each numeric type? Well, though it makes the package harder to maintain, having type specific integrators is a priority for me. I could have used interface-based integrators but it would be at the expense of the extensibility of the integrators to more custom numerical types, a feature which I find relevant too.

TEST

You can run all tests with

go test -v ./...   

or individual type oriented tests as

go test -v ./float64 # For float64 type   

To Do

• Support higher order methods.
• Implement adaptative step methods.

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,

float32
float64
complex64
complex128

The methods implemented so far are,

* Euler

* Mid point

* Runge-Kutta 4

The package is easily extensible to provide other methods, you can follow the template files as reference,

templates/stepper_method.go.t
templates/stepper_method_test.go.t

Example - Simple harmonic oscillator

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

There are more examples at the examples path

FAQ

A subpackage for each numeric type?

You might be thinking, why does this guy have a subpackage for each numeric type? Well, though it makes the package harder to maintain, having type specific integrators is a priority for me. I could have used interface-based integrators but it would be at the expense of the extensibility of the integrators to more custom numerical types, a feature which I find relevant too.

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.