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

• Euler Method applied to Linear Population Equation
• Euler Method applied to Non-Linear Population Equation

• Taylor Method applied to Non-Linear Population Equation

• Runge Kutta
• Runge Kutta applied to Population Equations

• Adam-Bashforth Method (explicit) applied to Population Equations

• Adams-Moulton Method (implicit) applied to Population Equations

• Predictor-Corrector Method

• Consistency
• Convergence
• Stability
• Further Notes on Consistency, Convergence and Stability

• Linear Shooting Method

• Non-Linear Shooting Method

• Finite Difference Method

• Explicit Finite Difference Method
• Implicit Finite Difference Methods
• Crank Nicolson

• Homogenous Equation
• Inhomogeneous Equation with zero boundary conditions
• Inhomogeneous Equation with non-zero boundary conditions

• Wave Equation
• Wave Equation Lax-Friedrich Method
• Wave Equation Lax-Wendroff Method
• Burger Equation

[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.

Strogatz. S., (2021, March 1). Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University [Video]. YouTube. https://www.youtube.com/playlist?list=PLbN57C5Zdl6j_qJA-pARJnKsmROzPnO9V

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

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.

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

Butler, J. S., (2021), Numerical Analysis Playlist https://open.spotify.com/embed/playlist/58fMf5qf9DGdrGqsY6laMS