newton, animation, semi-implicit euler method, gravity

Explaining the concept and simulating gravitational slingshot of a spacecraft passing a planet.

differential equation, ode, gravity, newton, 4th order runge-kutta, einstein, angular momentum, space

Discussion of orbits in the Schwarzschild Geometry.

Solving fixed-point problems using the Fix-Point Iteration method.

interpolation, animation, gravity, newton, 4th order runge-kutta, cubic splines

The motion of a rolling object on an arbitrary track is analyzed.

cavendish, curve fitting, harmonic oscillator, newton, gravity

Analyzes data from the Cavendish experiment using curve fitting. The Gravitational Constant is estimated.

bloch's theorem, newton's theorem, schrödinger equation

Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.

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.

animation, gravity, newton, embedded runge-kutta pair, angular momentum, space

Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.

newton, 4th order runge-kutta, space, lagrange, gravity

Studying how a third mass behaves in the effective gravitational potential resulting from two opposing masses (here: Sun and Earth).

newton, space, explicit euler method, gravity

Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.

chebychev nodes, newton, interpolation, lagrange, runges phenomenon

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

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