Easy to Implement Numerical Integrators for Fun and Profit
Mehmet Atakan Gürkan
Abstract: Numerical integration became an indispensable tool for solving problems in physics and other fields. Despite this, many researchers are satisfied with Euler's method and very few go beyond adaptive step size Runge-Kutta methods. In this talk, I will describe and develop a class of integrators that are very easy to implement and have other desirable properties, especially for long term integration of Hamiltonian flow problems. I will start with the simple leapfrog integrator and then generalize it to higher orders. By recasting this integrator as an operator, we can develop better integrators with similar properties. But we do not have to stop there; I will also demonstrate how the ``splitting'' formalism is useful for problems where we know the solution for the parts but not necessarily for the whole. The talk will be at colloquium level, i.e., a motivated sophomore should be able to follow most of the material, but even a graduate student will find something new.
Reminder: Tea and cookies will be in the seminar room before the seminar.