Experiments on Temporal Variable Step BDF2 Algorithms

Abstract

Efficient algorithms for solving stiff PDEs are of great interest. For developing such an algorithm step sizes should vary in both space and time. We have to understand each separately first before putting it together, and this thesis is dedicated to developing a sharper notion of the performance of a variable step size BDF2 scheme for some examples. We find suitable parameters for the variable step size algorithm proposed by Jannelli and Fazio in their respective paper concerning adaptive stiff solvers at low accuracy and complexity. Finally, we make a short excursion on the stability of BDF2 for the Allen-Cahn Equation.