Software for the design and analysis of time discretizations

In this talk I will describe and demonstrate two software packages Iâ ve developed as tools for research on time integration methods: Nodepy and RK-Opt. RK-Opt is a MATLAB package for optimizing properties of Runge-Kutta methods. It uses nonlinear optimization to find methods with optimized accuracy and stability properties with a given order, number of stages, and structure (explicit, implicit, diagonally implicit, low storage, etc.). It can be used to design specialized integrators tailored specifically to a class of PDE semi-discretizations. Nodepy (Numerical ODEs in Python) is a package for studying the properties of time integrators, including Runge-Kutta, linear multistep, extrapolation, and deferred correction methods. Given the coefficients of a method, it can provide a wealth of information on its accuracy and stability properties. It also includes basic tools for investigating a methodâ s efficiency in practical terms.Non UBCUnreviewedAuthor affiliation: Mathematical and Computer Sciences and EngineeringResearche