Numerical_Methods_Introduction

Interactive scripts for numerical methods course on MSc level. Comments and contributions are welcome.

Note: I’ve transitioned from interactive html pages created with nbinteract to a direct usage of mybinder. Starting any of the scripts may take a few minutes depending on when the last built took place.

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

All scripts

If you want to work with several scripts, launch the entire repository on mybinder.org via this link

Individual scripts:

If one of the specific scripts is of interest, you can launch them individually via the links below.

A naive introduction

Explicit Euler

Implicit Euler

Generalized mid point Picard

Generalized mid point Picard, nonlinear

Generalized mid point Newton

Generalized mid point Newton, nonlinear

Iteration schemes: Newton and Picard

Iteration schemes: arc length methods

Active earth pressure, Newton-Raphson

CPT tests and relative density, least squares

Ritz Galerkin collocation

Soil column FDM

Spatial discretization and integration

Soil column FEM

Terzaghi consolidation

Terzaghi consolidation, explicit

Terzaghi consolidation, Crank-Nicolson

Terzaghi consolidation, mass lumping

Terzaghi consolidation, mass lumping and finite increment calculus

Coupled problems

Localization in 1D

Freezing and thawing

Simple 2D FEM example of potential flow, nodal flow rate calculation

2D FEM TH coupled advection-diffusion problem

Some notes on Lagrange multipliers

Beam examples – collocation method

Beam examples – least squares method

Beam examples – subdomain method

Beam examples – Galerkin method