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https://github.com/soypat/godesim

ODE system solver made simple. For IVPs (initial value problems).
https://github.com/soypat/godesim

differential-equations dormand-prince golang initial-value-problem ivp newton-raphson-multivariable ode ode-solver runge-kutta runge-kutta-fehlberg simulation

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

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# godesim



Simulate complex systems with a simple API.

---



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



Note: [gonum/exp](https://github.com/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.



```console

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](./_examples)



### Quadratic Solution



```go

// 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:



![](_assets/quadratic_eq.png)



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



![](_assets/quadratic_eq_sol.png)



### How to obtain results

```go

// 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`](./_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](./_examples/simplePendulum)

* [Double pendulum exhibiting chaotic motion](./_examples/doublePendulum)

* [N-Body simulation](./_examples/n-body)



### 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.