Numerical Analysis with Applications in Python
This github consists of Python code corresponding to the course Numerical Analysis for Ordinary and Partial Differential Equations.
This is the JupyterBook for the code
If you have trouble viewing the jupyter files copy the link and paste into the nbviewer website
Part 1 Numerical Solutions to Ordinary Differential Equations
Chapter 1 Numerical Solutions to Initial Value Problems
- Euler Method applied to Linear Population Equation
- Euler Method applied to Non-Linear Population Equation
Chapter 2 Higher Order Methods
- Taylor Method applied to Non-Linear Population Equation
Chapter 3 Runge–Kutta methods
- Runge Kutta
- Runge Kutta applied to Population Equations
Chapter 4 Multi-step methods
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Adam-Bashforth Method (explicit) applied to Population Equations
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Adams-Moulton Method (implicit) applied to Population Equations
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Predictor-Corrector Method
Chapter 5 Analsyis of Methods for Initial Value Problems
- Consistency
- Convergence
- Stability
- Further Notes on Consistency, Convergence and Stability
Part 2 Numerical Solutions to Boundary Value Problems
Chapter 6 Boundary Value Problems
Part 3 Numerical Solutions to Partial Differential Equations
Chapter 8 Parabolic equations (Heat Equation)
- Explicit Finite Difference Method
- Implicit Finite Difference Methods
- Crank Nicolson
Chapter 9 Elliptic PDE’s (Poisson Equation)
- Homogenous Equation
- Inhomogeneous Equation with zero boundary conditions
- Inhomogeneous Equation with non-zero boundary conditions
Chapter 10 Hyperbolic Equations
- Wave Equation
- Wave Equation Lax-Friedrich Method
- Wave Equation Lax-Wendroff Method
- Burger Equation
References
[1] Strogatz, S. (2014) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity), Westview Press; 2 edition
[2] Bradie, B., (2006). A Friendly Introduction to Numerical Analysis. Pearson Education India.
[3] Atkinson, K. E., & Han, W. (1993). Elementary numerical analysis. New York: Wiley.
[4] Burden, R. L., Faires, J. D., (1997). Numerical Analysis. Brooks/Cole
[5] Stoer, J., & Bulirsch, R., (1980). Introduction to Numerical Analysis. Springer-Verlag
[6] Smith, G. D., (1992) Numerical Solution of Partial Differential Equations:Finite Difference Method. Oxford
[7] Sirca, S., Horvat, M., 2018, Computational Methods in Physics: Compendium for Students, Second Edition, Springer ISBN: 978-3-319-78619-3
[8] Brunton, S. L., & Kutz, J. N. (2019). Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press.
Supplementary Video Lectures
Strogatz. S., (2021, March 1). Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University [Video]. YouTube. https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V
Popular Videos
The Relationship Equation - Numberphile. (2015, April 3). [Video]. YouTube. https://www.youtube.com/watch?v=BkOIw7vAZCQ
How Wolves Change Rivers. (2014, February 13). [Video]. YouTube. https://www.youtube.com/watch?v=ysa5OBhXz-Q
Popular Press Reading
Tree, I. (2018). Wilding: The return of nature to a British farm. Pan Macmillan.
Strogatz, S. (2004). Sync: The emerging science of spontaneous order. Penguin UK.
Podcasts
Strogatz, S. (2019-2021). Joy of X. Quanta Magazine. https://www.quantamagazine.org/tag/the-joy-of-x
In Our Time, (2014). e, BBC Radio 4 https://www.bbc.co.uk/programmes/b04hz49f
Playlist
Butler, J. S., (2021), Numerical Analysis Playlist https://open.spotify.com/embed/playlist/58fMf5qf9DGdrGqsY6laMS
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