Theses and Dissertations

Issuing Body

Mississippi State University


Bhushan, Shanti

Committee Member

Collins, Eric M.

Committee Member

Sescu, Adrian

Date of Degree


Document Type

Graduate Thesis - Open Access


Computational Engineering

Degree Name

Master of Science (M.S.)


James Worth Bagley College of Engineering


Computational Engineering Program


The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit chaotic behavior. Promising results emerge and are presented in the form of a regression analysis across a parametric study of the Lorenz system.