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add fdm titles to table of content
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@mbarzegary
mbarzegary committed Jul 25, 2021
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Expand Up @@ -10,6 +10,8 @@ The mentioned repositores are embedded (and then partially modified) as [git sub

## Table of Content

0. [Introduction to Jupyter notebooks](2-finite-difference-method/lessons/00_getting_started/00_03_Intro_to_Jupyter_notebook.md)

### Scientific programming with Python

1. [Introduction to scientific computing with Python](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/1-scientific-programming/Lecture-0-Scientific-Computing-with-Python.ipynb)
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### Finite difference method for (partial) differential equations

9. Initial-value problems: solving nonlinear ordinary differential equations
* [Introducing the problem: the phugoid model of glider flight](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/01_phugoid/01_01_Phugoid_Theory.ipynb)
* [Solving a single-equation model of oscillation using Euler's method](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/01_phugoid/01_02_Phugoid_Oscillation.ipynb)
* [Solving a full phugoid model using vectorized Euler's method](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/01_phugoid/01_03_PhugoidFullModel.ipynb)
* [Higher-order methods: modified Euler and Runge-Kutta](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/01_phugoid/01_04_Second_Order_Methods.ipynb)
10. General aspects of numerical solution of partial differential equations
* [Discretizing equations: 1D linear convection](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/02_spacetime/02_01_1DConvection.ipynb)
* [Stability and the CFL condition](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/02_spacetime/02_02_CFLCondition.ipynb)
* [Discretizing 2nd-order derivatives: 1-D Diffusion](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/02_spacetime/02_03_1DDiffusion.ipynb)
* [Combining non-linear convection and diffusion: Burger's equation](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/02_spacetime/02_04_1DBurgers.ipynb)
11. Riding the wave: convection problems
* [Conservation laws and convection: solving a traffic flow model](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/03_wave/03_01_conservationLaw.ipynb)
* [Numerical schemes for hyperbolic partial differential equations](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/03_wave/03_02_convectionSchemes.ipynb)
* [A better flux equation for the traffic flow model](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/03_wave/03_03_aBetterModel.ipynb)
* [Introducing finite volume method](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/03_wave/03_04_MUSCL.ipynb)
12. Spreading out: diffusion problems
* [Parabolic partial differential equations: heat conduction](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/04_spreadout/04_01_Heat_Equation_1D_Explicit.ipynb)
* [Implicit schemes for the 1D heat equation](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/04_spreadout/04_02_Heat_Equation_1D_Implicit.ipynb)
* [2D Heat conduction and finite difference: explicit schemes](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/04_spreadout/04_03_Heat_Equation_2D_Explicit.ipynb)
* [2D Heat conduction: implicit solution](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/04_spreadout/04_04_Heat_Equation_2D_Implicit.ipynb)
* [Crank-Nicolson scheme](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/04_spreadout/04_05_Crank-Nicolson.ipynb)
13. Elliptic problems
* [Iterative solution: Jacobi method for Laplace equation](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/05_relax/05_01_2D.Laplace.Equation.ipynb)
* [2D Poisson equation](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/05_relax/05_02_2D.Poisson.Equation.ipynb)
* [Gauss-Seidel and successive over-relaxation (SOR) schemes](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/05_relax/05_03_Iterate.This.ipynb)
* [The method of conjugate gradients (CG)](https://nbviewer.jupyter.org/github/TuxRiders/numerical-computing-intro/blob/main/2-finite-difference-method/lessons/05_relax/05_04_Conjugate.Gradient.ipynb)


### Finite element method for (partial) differential equations

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