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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).

See https://nagelt.github.io

Comments and contributions are welcome.

Related publication:

Kern, D., & Nagel, T. (2022). An experimental numerics approach to the terrestrial brachistochrone. GAMM Archive for Students, 4(1), 29–35. https://doi.org/10.14464/gammas.v4i1.512

Kern, D., & Nagel, T. (2024). The essence of Biot waves in an oscillator with two degrees of freedom. GAMM Archive for Students, 6(1). https://doi.org/10.14464/gammas.v6i1.663