I. NUMERICAL ANALYSIS

Numerical Analysis I

1.

MATH 561: Numerical Analysis I

Problem 1 (Convergence of Richardson iteration). This method’s operator has the form T = I − BA = I − ωA because B = ωI. The eigenvectors of T are – as is easy to verify, the same as those of A, and the eigenvalues of T are λi(T ) = 1− ωλi(A). To prove that the method converges, it is convenient to verify that the l2 norm of T is less than one because we can then express everything in terms of ...

CAAM 453 Numerical Analysis I Rice University

I. Numerical simulations

A 1D loop radiative hydrodynamic model that incorporates the effects of gravitational stratification, heat conduction, radiative losses, external heat input, presence of helium, and Braginskii viscosity is used to simulate elementary flare loops. The physical parameters for the input are taken from observations of the Bastille-Day flare of 2000 July 14. The present analysis shows that: a) the o...

Numerical Simulations in Cosmology I

The purpose of these lectures is to give a short introduction into a very vast field of numerical simulations for cosmological applications. I focus on major features of the simulations: the equations, main numerical techniques, effects of resolution, and methods of halo identification.