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


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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.


Requires Go.

go get


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

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,
    "theta":  0,
    "theta-dot": 0,
sim.SetTimespan(0.0, 1.0, 10) // One second simulated

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.

Final notes

Future versions of gonum will have an ODE solver too. Ideally godesim would base it's algorithms on gonum's implementation. See 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.