/Numerical-Analysis-Python

Python notebooks for Numerical Analysis

Primary LanguageJupyter NotebookMIT LicenseMIT

Numerical Analysis with Applications in Python

This github consists of Python code coresponding to the course Numerical Analysis for Ordinary and Partial Differential Equations.

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

  • One-Step Methods
    • Euler Method applied to Linear Population Equation Open In Colab
    • Euler Method applied to Non-Linear Population Equation Open In Colab

Chapter 2 Higher Order Methods

  • Taylor Method
    • Taylor Method applied to Non-Linear Population Equation Open In Colab

Chapter 3 Runge–Kutta methods

  • Runge Kutta
  • Runge Kutta applied to Population Equations Open In Colab

Chapter 4 Multi-step methods

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

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

  • Predictor-Corrector Method Open In Colab

Chapter 5 Analsyis of Methods for Initial Value Problems

  • Consistency Open In Colab
  • Convergence Open In Colab
  • Stability Open In Colab
  • Further Notes on Consistency, Convergence and Stability Open In Colab

Part 2 Numerical Solutions to Boundary Value Problems

Chapter 6 Boundary Value Problems

  • Linear Shooting Method Open In Colab

  • Non-Linear Shooting Method Open In Colab

  • Finite Difference Method Open In Colab

Part 3 Numerical Solutions to Partial Differential Equations

Chapter 8 Parabolic equations (Heat Equation)

  • Explicit Finite Difference Method Open In Colab
  • Implicit Finite Difference Methods Open In Colab
  • Crank Nicolson Open In Colab

Chapter 9 Elliptic PDE’s (Poisson Equation)

  • Homogenous Equation Open In Colab
  • Inhomogeneous Equation with zero boundary conditions Open In Colab
  • Inhomogeneous Equation with non-zero boundary conditions Open In Colab

Chapter 10 Hyperbolic Equations

  • Wave Equation Open In Colab
  • Wave Equation Lax-Friedrich Method Open In Colab
  • Wave Equation Lax-Wendroff Method Open In Colab
  • Burger Equation Open In Colab

References

[1] Strogatz, S. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (studies in nonlinearity), Westview Press; 2 edition (29 July 2014)

[2] Brian Bradie, A Friendly Introduction to Numerical Analysis

[3] Atkinson, Han Elementary Numerical Analysis

[4] Richard L. Burden, J. Douglas Faires, Numerical Analysis, Brooks/Cole 1997

[5] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag 1980

[6] G D Smith Numerical Solution of Partial Differential Equations: Finite Difference Method Oxford 1992

Supplementary Video Lectures

Steven Strogatz. (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