https://github.com/louis-finegan/second-order-ode

Solving second order ODEs and Systems of ODEs with scipy library.
https://github.com/louis-finegan/second-order-ode

calculus eigenvalues equilibrium-point matplotlib numerical-integration numpy ordinary-differential-equations python python3 scipy

Last synced: 10 days ago
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Solving second order ODEs and Systems of ODEs with scipy library.

• Host: GitHub
• URL: https://github.com/louis-finegan/second-order-ode
• Owner: Louis-Finegan
• Created: 2023-02-07T14:01:37.000Z (about 2 years ago)
• Default Branch: master
• Last Pushed: 2023-11-21T11:44:54.000Z (about 1 year ago)
• Last Synced: 2024-12-06T09:10:23.275Z (2 months ago)
• Topics: calculus, eigenvalues, equilibrium-point, matplotlib, numerical-integration, numpy, ordinary-differential-equations, python, python3, scipy
• Language: Python
• Homepage: https://github.com/Louis-Finegan/Second-Order-ODE
• Size: 677 KB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Second Order ODEs and Systems of ODEs with `SciPy`

## Solves a second order Linear ODE 

Takes the form:

$$\frac{d^2y}{dt^2} + a(t)\frac{dy}{dt} + b(t)y = c(t)$$

With initial conditions $y(0) = y_0$ and $y^\prime(0) = y^\prime_0$.

Coefficients are functions of $t$ and are defined in `second_order.ipynb`

`second_order_ode` module in the `solve.py` file in the `ode` directory, and is imported into `second_order.ipynb`.

## Solves a First Order System of ODEs

Takes the form:

$$\frac{dx}{dt} = F(x, y)$$

$$\frac{dy}{dt} = G(x, y)$$

With initial conditions $x(0) = x_0$ and $y(0) = y_0$.

$F$ and $G$ are defined in `first_order_system.ipynb`.

`first_order_system_2vars` module in the `solve.py` file in the `ode` directory, and is imported into `first_order_system.ipynb`.

Then for 3 variable systems, use the module `first_order_system_3vars`.

 

## Required packages and libaries

1. `numpy`

2. `scipy` using the `integrate` module 

3. `scipy` using the `optimize` module 

3. `matplotlib` using the `pyplot` module