ODEs

Tutorial (TD) and practical work (TP) notebook file can be downloaded here:

• ODE_pendulum.ipynb
• ODE_harmonic_oscillator.ipynb

• Ordinary differential equations (ODE)
  • Scope
  • Ordinary differential equations vs. partial differential equation
    • Ordinary differential equations (ODE)
    • Partial differential equations (PDE)
  • Introductive example
  • Closed form solution
  • Reformulation
  • Numerical integration of ODE
  • Euler method
  • Runge Kutta 4
  • Using ODEint
  • Tutorial (TD)
• Tutorial: The simple pendulum
  • Introduction
    •  Numerical values
  • Part 1: Reformulation of the problem
  • Part 3: Numerical solution
  • Part 4: Energies an errors
• Ordinary Differential Equations : Practical work on the harmonic oscillator
  • Theory
    • Mechanical oscillator
    • Canonical equation
    •  Undampened oscillator
  • Part 1: theoretical solution
  • Part 2: Numerical solution with Euler integrator
  • Part 3: Energies an errors
  • Part 4: Numerical solution convergence
  • Part 5: integrator benchmark
  • Part 6: Error vs. time
• Ordinary differential equations: solar system