# Computational Methods for PDE's II

## ES 205: Spring Term 2009

This is my personal web site for ES 205: Computational Methods for Partial Differential Equations II with Prof. Keith Paulsen offered in the Spring term of 2009. On this website you will find relevant material used and presented in this course.

## Homeworks

• HOMEWORK #4:
This is the second of two problem sets using spectral methods. In THIS problem set we solved Burgers equation using the pseudospectral and the collocation methods. This is a classic PDE problem where we compared our numerical results to our analytical solution.

Matlab Code

@ t = p/8

@ t = 2*p/8

• HOMEWORK #3:
This is the first of two problem sets using spectral methods. In THIS problem set we were asked to test out the Finite Difference, Finite Element, and two spectral methods and compare their results against the analytical solution to a first derivative problem seen here.

Matlab Code

FINITE DIFFERENCE METHOD

FINITE ELEMENT METHOD

COLLOCATION SPECTRAL METHOD

MATRIX SPECTRAL METHOD

• HOMEWORK #2: April 27, 2009
Use the Boundary Element Method to solve THIS problem, a continuation on homework assignment #1, with a small variation on "Treatment of Corners." The computations were done with Fortran and plotting with Matlab. Thanks to Lyubomir, Xiaoyao, Amir, and Matt.

Fortran Source Code Part 1

Fortran Source Code Part 2

Matlab Plotting Routine

SOLUTION, "PART 1 "

VECTORS, "PART 1 "

SOLUTION, "STRATEGY #2 "

VECTORS, "STRATEGRY #2 "

SOLUTION DIFFERENCE, "PART 1 VS STRATEGY #2 "

• HOMEWORK #1: April 17, 2009
Use the Boundary Element Method to solve THIS problem. The computations were done with Fortran and plotting with Matlab. Thanks to Lyubomir, Xiaoyao, Amir, and Matt.

Fortran Source Code

Matlab Plotting Routine

SOLUTION WITH FORCING

SOLUTION WITH FORCING 3D

SOLUTION VECTORS