Numerical algorithms for differential equations with periodicity

Thesis

This thesis presents new numerical methods for solving differential equations with periodicity.

Spectral methods for solving linear and nonlinear ODEs, linear ODE eigenvalue problems and linear time-dependent PDEs on a periodic interval are reviewed, and a novel approach for computing multiplication matrices is presented.

Choreographies, periodic solutions of the n-body problem that share a common orbit, are computed for the first time to high accuracy using an algor...

Expand abstract

Authors: Montanelli, H

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Keywords: PDEs on the sphere; Choreographies; Periodic Differential Equations; Stiff PDEs; Nonlinear ODEs; Stiff ODEs; Fourier spectral methods
• Subjects: Numerical Mathematics; Applied Mathematics; Numerical PDEs; Applied PDEs