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

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

john-s-butler-dit/Numerical-Analysis-Python