### MA 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.

### MIDERM: No Midterm in Spring semester 2021

**FINAL PROJECT**

*(Please attach a copy of your source code and instructions so I can run your code)*