gds-continuous¶

Continuous-time ODE integration engine -- the continuous-time counterpart to gds-sim.

What is this?¶

gds-continuous provides an ODE simulation engine for continuous-time dynamical systems. It follows the same standalone architectural pattern as gds-sim -- minimal dependencies, Pydantic models, columnar results -- but integrates SciPy's ODE solvers instead of discrete timestep iteration.

ODEModel -- declares state variables, initial conditions, and a right-hand side function dx/dt = f(t, x, params)
ODESimulation -- configures time span, solver method, tolerances, and evaluation points
ODEResults -- columnar storage of time series with named state access
6 solver methods -- RK45, RK23, DOP853, Radau, BDF, LSODA (all via scipy.integrate.solve_ivp)
Zero GDS dependency -- standalone package, same as gds-sim

Architecture¶

scipy + numpy (optional deps)
|
+-- gds-continuous (uv add gds-continuous[scipy])
    |
    |  ODE engine: ODEModel, ODESimulation, ODEResults.
    |  6 solver backends via scipy.integrate.solve_ivp.
    |
    +-- Your application
        |
        |  Concrete ODE models, parameter studies,
        |  phase portraits, trajectory analysis.

Relationship to gds-sim¶

	gds-sim	gds-continuous
Time	Discrete timesteps	Continuous `t_span`
Update rule	`f(state, params) -> state`	`dx/dt = f(t, x, params)`
Solver	Direct iteration	SciPy `solve_ivp`
Results	`Results` (timestep-indexed)	`ODEResults` (time-indexed)
Dependencies	pydantic only	pydantic + scipy + numpy

Both are standalone engines with no gds-framework dependency. They can be used independently or bridged via gds-analysis.

Solver Methods¶

Method	Type	Best for
`RK45`	Explicit Runge-Kutta (default)	General non-stiff problems
`RK23`	Explicit Runge-Kutta	Low-accuracy requirements
`DOP853`	Explicit Runge-Kutta	High-accuracy non-stiff problems
`Radau`	Implicit Runge-Kutta	Stiff problems
`BDF`	Implicit multi-step	Stiff problems
`LSODA`	Automatic stiff/non-stiff	Unknown stiffness

Quick Start¶

uv add "gds-continuous[scipy]"

See Getting Started for a full walkthrough.

Credits¶

Built by BlockScience.