https://github.com/kkawula/heat-transfer-fem

Differential equation solver
https://github.com/kkawula/heat-transfer-fem

Last synced: about 2 months ago
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Differential equation solver

• Host: GitHub
• URL: https://github.com/kkawula/heat-transfer-fem
• Owner: kkawula
• Created: 2024-01-18T16:15:10.000Z (about 1 year ago)
• Default Branch: main
• Last Pushed: 2024-01-18T18:22:31.000Z (about 1 year ago)
• Last Synced: 2024-06-27T01:01:34.782Z (7 months ago)
• Language: Python
• Homepage:
• Size: 104 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Finite Element Method (FEM) for Heat Transfer Equation

$$

\frac{d}{dx} \left( k(x)  \frac{du(x)}{dx}\right) = -100x

$$

$$

u(2) = 0

$$

$$

\frac{du(0)}{dx} + u(0) = 20

$$

$$

k(x) = \begin{cases}

  1 & \text{for } x \in [0,1] \\

  2x & \text{for } x \in (1,2]

\end{cases}

$$

$$

\text{Where } u \text{ is the function you are looking for}

$$

$$

[0,2] \ni x \mapsto u(x) \in \mathbb{R}

$$

### Requirements

Python, `numpy`, `matplotlib`, and `scipy`.