Numerical Analysis with Applications in Python#

This is Jupyterbook for the course notes Numerical Analysis for Ordinary and Partial Differential Equations.

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Concept Map for the materials\label{mylabel}

Part 1 Numerical Solutions to Ordinary Differential Equations#

Chapter 1 Numerical Solutions to Initial Value Problems#

  • 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 applied to Non-Linear Population Equation Open In Colab

Chapter 3 Runge–Kutta methods#

  • 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

Podcasts#

Strogatz, S. (2019-2021). Joy of X. Quanta Magazine. https://www.quantamagazine.org/tag/the-joy-of-x