These slides and files are for a two-day short course on Numerical Analysis of Singularly Perturbed Differential Equations, taught by Niall Madden as part of the 2016 AARMS-CRM Workshop on Numerical Analysis of Singularly Perturbed Differential Equations July 25-29, 2016, Halifax, NS, Canada.
These are drafts of the slides. If you see plot any errors or typos, please contact Niall.
Slides and files | ||||
Section 0. | Outline of the workshop | Slides | ||
Section 1. | Introduction to singularly perturbed problems | Slides | Handout | |
Section 2. | Numerical methods and uniform convergence; FDMs and their analysis. | Slides | Handout | |
Section 3. | Coupled systems | Slides | Handout | |
Section 4. | Lab 1: Singularly perturbed ODEs | MATLAB primer | Files: FiniteDifference.m | |
Handout | Files: Make_1D_Fitted_Mesh.m, Solve_1DRD.m, Test_1DRD.m, u_true.m. | |||
Solutions | Files: Make_1D_CD_Mesh.m, Solve_1DCD.m, Test_1DCD.m | |||
Section 5. | PDEs (i): Time-dependent problems | Slides | Handout | |
Section 6. | PDEs (ii): elliptic problems in two-dimensions | Slides | Handout | |
Section 7. | Finite Element Methods | Slides | Handout | |
Section 8. | Lab 2: Singularly perturbed PDEs | Handout | Files: Solve_2DRD.m, Test_2DRD.m, Problem_Data.m, Make_Bakhvalov_Mesh.m. |