https://github.com/samya-s/modeling-and-simulation-lab
Modeling and Simulation Lab (MA39206)
https://github.com/samya-s/modeling-and-simulation-lab
mathematical-modelling mathematical-modelling-and-simulation modeling modeling-and-simulation modelling modelling-and-simulation simulation
Last synced: 3 months ago
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Modeling and Simulation Lab (MA39206)
- Host: GitHub
- URL: https://github.com/samya-s/modeling-and-simulation-lab
- Owner: Samya-S
- License: mit
- Created: 2025-01-10T13:54:00.000Z (4 months ago)
- Default Branch: main
- Last Pushed: 2025-02-15T14:28:09.000Z (3 months ago)
- Last Synced: 2025-02-15T15:30:01.925Z (3 months ago)
- Topics: mathematical-modelling, mathematical-modelling-and-simulation, modeling, modeling-and-simulation, modelling, modelling-and-simulation, simulation
- Language: Jupyter Notebook
- Homepage:
- Size: 2.01 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Modeling and Simulation Lab (MA39206)
**L-T-P:** 0-0-3 | **Credits:** 2
**Prerequisites:**
- Ordinary Differential Equations
- Partial Differential Equations
- Mathematical Modeling
## Syllabus
### 1. Population Dynamics Models
- Numerical simulation of simple one-variable population models and continuous growth models.
- Simulations of delay models and age distribution models.
- Linear stability analysis of nonlinear systems.
**[2 Labs]**
### 2. Ecological Models
- Simulation of Predator–Prey Models: Lotka–Volterra Systems.
- Complexity and stability analysis of predator–prey models with limit cycles.
- Periodic behavior and parameter domains of stability in competition models.
**[2 Labs]**
### 3. Epidemiology Models
- Simulation of epidemic models: SIS, SIR Epidemics, and SIR Endemics in MATLAB.
- Tumor models: Simulation of tumor spread and invasion in the human brain.
- Numerical computation for different treatment scenarios.
**[2 Labs]**
### 4. Numerical Simulation of Physical Processes
- Linear elasticity problems and Hooke’s Law.
- 2D Inviscid flow models: Simulation of streamlines, streaklines, and pathlines.
- Viscous flow models: Navier-Stokes Flow, Newtonian and Non-Newtonian flow through pipes (Hagen-Poiseuille flow, Couette flow).
**[5 Labs]**
### 5. Simulation of Diffusion-Reaction Processes
- Chemical reactions and the Mass Action Law.
- Kinetic reactions: 0th, 1st, and nth order.
- Convection-reaction-diffusion models.
- Heat conduction and solute dispersion.
- Exact solutions of convection-diffusion-reaction models.
**[2 Labs]**
## References
1. C. Eck, H. Garcke, and P. Knabner: *Mathematical Modeling*, Springer, 2017.
2. R. Temam and A.M. Miranville: *Mathematical Modelling in Continuum Mechanics*, Cambridge University Press, 2001.
3. J.D. Murray: *Mathematical Biology Vol. I & II*.
4. A. Friedman and C. Chou: *Introduction to Mathematical Biology*.
## How to Use this Repository
Clone this repository:
```bash
git clone https://github.com/Samya-S/Modeling-and-Simulation-Lab.git
```
## License
This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.