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Introduction to numerical methods using Jupyter Notebooks

A set of Jupyter Notebooks demonstrating various numerical methods in Python. Among those are:

  • Single-step time integration: Euler forward and backward, Crank-Nicolson.
  • Finite difference, finite element, collocation, subdomain, least-squares methods
  • Iterative Picard and Newton-Raphsons solution methods
  • Stabilization methods: Mass lumping and finite increment calculus
  • First aspects of localization of softening material models
  • Concepts of staggered and monolithic coupling schemes

Illustrative examples chosen include first order models, beam bending theories and Terzaghi consolidation.

The notebooks mainly make use of

  • numpy
  • scipy
  • matplotlib
  • ipywidgets
  • sympy

The latter allows an interactive adaptation of parameters to immediatly illustrate their effect, e.g. the time-step size.

The notebooks can be viewed with nbviewer, see https://jupyter.org/, or can now also be run interactively using binder (available through nbviewer).

Comments and contributions are welcome.

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A set of Jupyter Notebooks demonstrating various numerical methods in Python.

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