Homework APMA 2560

Homework APMA 2560

 

Homework 1

1. Write a code to solve the one-dimensional linear advection equation in the domain x in [-1,1] with periodic boundary conditions. We are interested in studying the phase properties of finite differences on non-equidistant grids, so construct grids that coarsen linearly from x=0 to the two ends at -1 and +1 at a specified coarsening factor.

2. Analyze the phase error numerically for second-, fourth-, sixth- and tenth-order FD derivative as a function of the coarsening factor. That is, prepare plots that show how the phase error grows in time for different values of the coarsening factor. You can choose a sufficiently large number of grid points so that your results are still accurate after long time integration.

Homework 2

Homework 3

Homework 4