Theses and Dissertations

Issuing Body

Mississippi State University


Luke, Edward A.

Committee Member

Soni, Bharat K.

Committee Member

Cinnella, Pasquale

Date of Degree


Document Type

Graduate Thesis - Open Access


Computational Engineering (Program)

Degree Name

Master of Science


This study seeks to reduce the cost of numerically solving non-linear partial differential equations by reducing the number of computations without compromising accuracy. This was done by using accurate local time stepping. This algorithm uses local time stepping but compensates for the inconsistencies in the temporal dimension by interpolations and/or extrapolations. Reduction in computations are obtained by time-stepping only a particular region with small time steps. A shock tube problem and a detonation wave were the two test cases considered. The performance of the solution using this algorithm was compared with an algorithm that does not use accurate local time stepping.