Solving fixed-point problems using the Fix-Point Iteration method.
Using Newton's method to calculate the band structure for the simple Dirac comb potential in one dimension.
Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.
Applying the fourth order Runge-Kutta method and the adaptive step size Runge-Kutta method to calculate the trajectories of three bodies.
Studying how a third mass behaves in the effective gravitational potential resulting from two opposing masses (here: Sun and Earth).
Applying the explicit and implicit Euler methods and the fourth order Runge-Kutta method to calculate the trajectory of the Earth around the Sun.
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.
Determining a root with the Newton-Raphson algorithm.