ivp 0.5.1

A Rust library for solving initial value problems (IVPs) for ordinary differential equations (ODEs).
Documentation 
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<p align="center">
  <img src="./assets/logo.svg" width="1000" alt="ivp">
</p>

<p align="center">
    <a href="https://crates.io/crates/ivp">
        <img src="https://img.shields.io/crates/v/ivp.svg?style=flat-square" alt="crates.io">
    </a>
    <a href="https://pypi.org/project/ivp-rs/">
        <img src="https://img.shields.io/pypi/v/ivp-rs.svg?style=flat-square" alt="PyPI">
    </a>
    <a href="https://docs.rs/ivp">
        <img src="https://docs.rs/ivp/badge.svg" alt="docs.rs">
    </a>
    <a href="https://github.com/Ryan-D-Gast/ivp/blob/main/LICENSE">
        <img src="https://img.shields.io/badge/License-Apache%202.0-blue.svg">
    </a>
</p>

<p align="center">
    <strong>
        <a href="https://docs.rs/ivp/latest/ivp/">Documentation</a> |
        <a href="./examples/">Examples</a> |
        <a href="https://github.com/Ryan-D-Gast/ivp">GitHub</a> |
        <a href="https://crates.io/crates/ivp">Crates.io</a> |
        <a href="https://pypi.org/project/ivp-rs/">PyPI</a>
    </strong>
</p>

-----

<p align="center">
<b>A library of numerical methods for solving initial value problems (IVPs)</b><br>
<i>for Rust and Python.</i>
</p>

-----

This library provides a pure Rust implementation of SciPy's `solve_ivp` function with slight modifications to the API to better fit Rust's design patterns. It is also available as a Python package with a SciPy-compatible API.

## Features


Currently implemented solvers:
-   **DOP853**: An 8th order Dormand-Prince method with step-size control and dense output.
-   **DOPRI5**: A 5th order Dormand-Prince method with step-size control and dense output.
-   **RK4**: The classic 4th order Runge-Kutta method with fixed step-size and cubic Hermite interpolation for dense output.
-   **RK23**: A 3rd order Runge-Kutta method with 2nd order error estimate for step-size control.
-   **Radau**: A 5th order implicit Runge-Kutta method of Radau IIA type with step-size control and dense output.
-   **BDF**: A variable-order (1 to 5) Backward Differentiation Formula method for stiff ODEs with adaptive step-size control and dense output.

## Installation


### Rust


```bash
cargo add ivp
```

### Python


```bash
pip install ivp-rs
```

## Example Usage (Python)


```python
from ivp import solve_ivp
import numpy as np

def exponential_decay(t, y):
    return -0.5 * y

# Solve the ODE

sol = solve_ivp(exponential_decay, (0, 10), [1.0], method='RK45', rtol=1e-6, atol=1e-9)

print(f"Final time: {sol.t[-1]}")
print(f"Final state: {sol.y[:, -1]}")
```