McMaster University Menu Search
Faculty of Science School of Computational Science and Engineering
Faculty of Science

School of Computational Science and Engineering

Differentiation Matrices for Fun & Profit

Taking derivatives - the action of differentiation - is a fundamental operation in the mathematics of functions, and because of that it is astonishingly useful in Science and Engineering (maybe the causation goes the other way). There are an equally astonishing number of methods to take derivatives in various situations, including "by hand" symbolic methods, computer-assisted symbolic methods (this pre-dates FORTRAN), finite differences (these pre-date computers), compact finite differences, automatic differentiation (forward and reverse mode), complex methods, and - the subject of the talk - differentiation matrices.
 
These are useful for solving ODE, PDE and oscillatory integrals. In this talk I will introduce differentiation matrices and contrast their use with other methods. I'll explain some universal properties, and show some niche methods.
 
I'll end by using them to evaluate some highly oscillatory integrals by Levin-type methods.
 
This is joint work with Amir Amiraslani (U. Hawaii) and Jeet Trivedi.
McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
School of Computational Science and Engineering

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.24116
Graduate Email Inquiries:
graduate@math.mcmaster.ca

McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
School of Computational Science and Engineering

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.24116
Graduate Email Inquiries:
graduate@math.mcmaster.ca

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa