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

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

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

• 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

• Linear Shooting Method

• Non-Linear Shooting Method

• Finite Difference Method

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