soypat/godesim

ODE system solver made simple. For IVPs (initial value problems).

godesim

Simulate complex systems with a simple API.

Wrangle non-linear differential equations while writing maintainable, simple code.

Note: gonum/exp is still in early development but offers a more flexible and lightweight alternative to godesim's full fledged simulator.

Why Godesim?

ODE solvers seem to fill the niche of simple system solvers in your numerical packages such as scipy's odeint/solve_ivp.

Among these integrators there seems to be room for a solver that offers simulation interactivity such as modifying the differential equations during simulation based on events such as a rocket stage separation.

Installation

Requires Go.

go get github.com/soypat/godesim

Progress

Godesim is in early development and will naturally change as it is used more. The chart below shows some features that are planned or already part of godesim.

Status legend	Planned	Started	Prototype	Stable	Mature
Legend symbol	✖️	🏗️	🐞️	🚦️	✅️

Features	Status	Notes
Non-linear solvers	🚦️	Suite of ODE solvers available.
Non-autonomous support	🚦️	U vector which need not a defined differential equation like X does.
Event driver	🚦️	Eventer interface implemented.
Stiff solver	🚦️	Newton-Raphson algorithm implemented and tested.

Algorithms available and benchmarks

Algorithm	Time/Operation	Memory/Op	Allocations/Op
RK4	1575 ns/op	516 B/op	12 allocs/op
RK5	2351 ns/op	692 B/op	21 allocs/op
RKF45	3229 ns/op	780 B/op	25 allocs/op
Newton-Raphson	8616 ns/op	4292 B/op	92 allocs/op
Dormand-Prince	4365 ns/op	926 B/op	32 allocs/op

Examples

Quadratic Solution

// Declare your rate-of-change functions using state-space symbols
Dtheta := func(s state.State) float64 {
	return s.X("theta-dot")
}

DDtheta := func(s state.State) float64 {
    return 1
}
// Set the Simulation's differential equations and initial values and hit Begin!
sim := godesim.New() // Configurable with Simulation.SetConfig(godesim.Config{...})
sim.SetDiffFromMap(map[state.Symbol]state.Diff {
    "theta":  Dtheta,
    "theta-dot": DDtheta,
})
sim.SetX0FromMap(map[state.Symbol]float64{
    "theta":  0,
    "theta-dot": 0,
})
sim.SetTimespan(0.0, 1.0, 10) // One second simulated
sim.Begin()

The above code solves the following system:

for the domain t=0 to t=1.0 in 10 steps where theta and theta-dot are the X variables. The resulting curve is quadratic as the solution for this equation (for theta and theta-dot equal to zero) is

How to obtain results

// one can then obtain simulation results as float slices 
t := sim.Results("time")
theta := sim.Results("theta")

Other examples

To run an example, navigate to it's directory (under examples) then type go run . in console.

There are three simple examples which have been cooked up and left in _examples directory. I've been having problems running Pixel on my machine so the simulation animations are still under work.

• Simple pendulum
• Double pendulum exhibiting chaotic motion
• N-Body simulation

Final notes

Future versions of gonum will have an ODE solver too. Ideally godesim would base it's algorithms on gonum's implementation. See https://github.com/gonum/exp ode package.

Contributing

Pull requests welcome!

This is my first library written for any programming language ever. I'll try to be fast on replying to pull-requests and issues.

godesim's Issues

Timespan struct

Since it's inception, the Timespan struct has been a patch to a bigger problem in godesim. There really is not much control over the domain in which the equations are integrated. Steps are a fixed size unless using an adaptive timestep method, and even then the method will choose the domain division. One can get around this by using events, which is OK for the most part, except for all the extra code.

Timespan really does not do much, it just suggests a timestep and a end time. If there is a more elegant solution, and there most certainly is, the difficulty would probably be adapting present day godesim's Timespan API usage to a new API.

The name is also a source of bother to me, I wish I had named it Domain, since there is no reason godesim only solves time-domain problems.