Date of Award

Spring 5-2015

Embargo Period

8-31-2015

Degree Type

Dissertation (CMU Access Only)

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Advisor(s)

Roy Nicolaides

Abstract

In this thesis, we consider the use of the sparse grid combination technique with finite difference methods to solve parabolic partial differential equations. Convergence results are obtained in L2 for arbitrary dimensions via Fourier analysis arguments under the assumption that the initial data lies in the Sobolev space H4 mix. Numerical results are presented for model problems and for problems from the field of option pricing.

Share

COinS