These slides and files are for the section of the GIAN Workshop on Theory and Computation of Singularly Perturbed Differential Equations taught by Niall Madden, at IIT (BHU), Varanasi, December 4-8, 2017.
These are drafts of the slides. If you see plot any errors or typos, please contact Niall.
Slides and files | ||||
Lecture 0 | Outline of the workshop | NM | Slides | |
Lecture 1 | Introduction to singularly perturbed problems | NM | Slides | |
Lecture 2 | Numerical methods and uniform convergence. | NM | Slides | |
Prelude to Lab 1 | NM | MATLAB primer | ||
Lab 1 | FDMs on Uniform Meshes | NM | Handout | Files: FiniteDifference.m |
Lecture 3 | Finite difference methods and their numerical analysis. | NM | Slides | |
Lecture 4 | Coupled systems | NM | Slides | |
Lab 2 | Fitted mesh methods for ODEs | NM | Handout | Files: Solve_1DRD.m, Make_1D_Fitted_Mesh.m, Test_1DRD.m, u_true.m. |
Lecture 5 | High order numerical methods for singularly perturbed problems | SK | ||
Lecture 6 | Singularly perturbed parabolic problems in 1D | SK | ||
Lecture 7 | Regular and singular perturbation methods | LPS | ||
Lab 3 | High-order methods | SK | ||
Lecture 8 | Singularly perturbed elliptic PDEs | NM | Slides | |
Lecture 9 | Finite Element Methods in two and three dimensions | NM | Slides Handout | |
Lab 4 | Singularly perturbed PDEs | NM | Handout | Files: Solve_2DRD.m, Test_2DRD.m, Problem_Data.m, Make_Bakhvalov_Mesh.m. Make_Equidistribute_Mesh.m. |
Lecture 10 | Preconditioning for singularly perturbed problems | NM | Slides | |
Details of remaining sessions to follow |