Search: ode

16 results

Astrophysics 1

  Precession of Mercury

ode, gravity, 4th order runge-kutta, einstein, angular momentum, space, fortran, extrapolation, f2py

Computes the precession of Mercury by linear extrapolation.

Mechanics 2

  Double Pendulum and Chaos

differential equation, animation, Lagrangian, Euler-Lagrange equations, chaos, phase space, odeint

Discusses the chaotic motion of the double pendulum using a phase-space diagram

  Simple Pendulum

animation, ode, explicit euler method

Simulates the simple pendulum and damped simple pendulum

Astrophysics 1

Curve Fitting 1

Thermodynamics 1

  One-dimensional Stationary Heat Equation

chebychev nodes, temperature

Solving the one-dimensional stationary heat equation with a Gaussian heat source by approximating the solution as a sum of Lagrange polynomials.

Biophysics 1

  The Fiber Bundle Bridge Model

polymer, hemmer, hansen, lennard-jones potential, sparse matrix, nygård, elasticity

Simulates the disentanglement of a polymer from a surface using an increasing electric field

Statistical Mechanics 1

  Ising Model in 1D and 2D

specific heat, partition function, magnetism, spin

Computing the internal energy, specific heat and magnetisation in the 1D and 2D Ising model. An analytical solution to the XY model is also provided.

Waves and Acoustics 1

  Sloshing

euler, eigenvalue, poisson's equation, integration, interpolation, newton, simpson's method

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

Curve Fitting 1

  Polynomial Interpolation

chebychev nodes, newton, interpolation, lagrange, runges phenomenon

Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.

Ordinary Differential Equations 5

  Adaptive Runge-Kutta Methods

4th order runge-kutta, trapezoidal method, ode, explicit euler method

Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.

  Runge-Kutta Methods

4th order runge-kutta, ode, explicit euler method

Solving a first-order ordinary differential equation using the Runge-Kutta method.

  Implicit Euler Method

euler, ode

Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).

  Euler's Method

ode, explicit euler method

Solving a first-order ordinary differential equation with Euler's method.

  Verlet Integration

ode

Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.

Chemistry 1

  Lennard-Jones Potential

explicit euler method, lennard-jones potential

A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.