Rheo: Declarative ODE Solver Interface

1. Define the System (ODE Definition)

Define the continuous state vector $\mathbf{x}(t)$ and its governing derivative $\frac{d\mathbf{x}}{dt} = \mathbf{f}(\mathbf{x}, t)$.

State Vector (e.g., [x, v]): Derivative Function (f(x, t)):

2. Execution Block & Constraints

Configure the temporal domain and accuracy invariants.

Time Domain (t_start to t_end): Absolute Tolerance (atol): Relative Tolerance (rtol): Stiffness Monitoring:

3. Results (Dense Output)

Awaiting simulation execution...

Rheo Philosophy Note: This interface models the core principle: defining the *derivative* ($\frac{dx}{dt}$) is the primitive, not the accumulation of steps. The system relies on Automatic Differentiation (AD) and Dynamic Method Selection to guarantee the Accuracy Invariant ($|\text{LTE}| \leq \max(\text{atol}, \text{rtol} \cdot |x|)$).