From 25bc8fc0a53cb709941785c1dc811f8d018e67fe Mon Sep 17 00:00:00 2001 From: mbarzegary Date: Sun, 25 Jul 2021 17:25:07 +0200 Subject: [PATCH] add fdm titles to table of content --- .gitignore | 1 + README.md | 28 ++++++++++++++++++++++++++++ 2 files changed, 29 insertions(+) create mode 100755 .gitignore diff --git a/.gitignore b/.gitignore new file mode 100755 index 0000000..ce420d1 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +.ipynb_checkpoints/ diff --git a/README.md b/README.md index 1f04124..bc7ff15 100755 --- a/README.md +++ b/README.md @@ -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) @@ -23,6 +25,32 @@ The mentioned repositores are embedded (and then partially modified) as [git sub ### 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