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.

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.

Requires Go.

go get github.com/soypat/godesim

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.

// 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

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

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

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.

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.