Course Materials for Math/AMath 596: Numerical Solution of Integral Equations

Syllabus: postscript format, or html

Assignments and handouts.

First homework assignment due Wed., Apr. 18: postscript format, or html

Second homework assignment due Wed., Apr. 25: postscript format, or html

Third homework assignment due Wed., May 9: postscript format, or html

Sample MATLAB codes.

Code to solve Laplace's equation inside an ellipse. lap2d_int.m
Uses boundary points that are equally spaced in theta, not arclength, and therefore is only second order accurate. Solves linear system directly.

Code to solve Laplace's equation inside an ellipse. lap2d_int_equal.m
Uses functions: inteval.m and spacing.m
Uses boundary points that are equally spaced in arclength (to within about 1.e-8), and therefore converges superalgebraically to this tolerance. Solves linear system directly.

Code to solve Laplace's equation outside an ellipse. lap2d_ext.m
Uses boundary points that are equally spaced in theta, not arclength, and therefore is only second order accurate. Solves linear system using MATLAB routine GMRES.

Code to implement Mayo's method of computing the solution to Laplace's equation on points throughout a lattice, by first solving an integral equation to determine jumps in the solution and its derivatives and then using a fast Poisson solver on an embedding rectangle. Code written by Michal Skokan. The main code is p1.m . It uses the following files: f.m , fprime.m , f_sec.m , mgres.m , mu_nul.m , mu_prime.m , mu_sec.m , mu_xx.m .