Doctoral Dissertations

Current and Past PhD students in Computational Science Program at MTSU

Currently three PhD students are working on Data Driven  Models and solving PDEs with deep learning.

•  Jie Long, Deep learning Algorithms for multidimensional partial differential equations in ecology, expected graduation, May 2025.
• Thomas Torku, Deep Neural Networks for Mathematical Models of Infection diseases, expected graduation, May 2024
• K. D. Olumoyin, Data-Driven Deep Learning Algorithms for Bio-Chemical and Epidemiology Models, May 2022. 
• A. Harris, Fractional Calculus in Population Dynamics, September 2021
• T.  A. Biala, Linealry Implicit Algorithms for Fractional PDEs, Spring 2020.
• S. S. Alzaharani, Numerical approximations for the fractional Laplacian in space-fractional reaction-diffusion equations, Dec. 2019.
• H.J. Lay, Stochastic Simulation using Multiple GPUs, Dec. 2019.
• V. Reshniak, Acceleration of the Multilevel Monte Carlo method for certain classes of differential systems, May 2017.
• Z. Colgin, Simulation of Stochastic Systems with MLMC, August 2016.
• H. Bhatt, Efficient and Accurate Exponential tTme Differencing Schemes for Systems of Nonlinear Time Dependnet Partial Differential Equations, August 2016.
• X. Liang, Efficient Numerical Methods for Non-linear Schrodinger Equations, December 2015.

Past PhD students jointly supervised

• Ibrahim Sarumi, co-advisor (jointly with Prof. Khaled Furati, KFUPM, Saudi Arabia); Generalized Exponential Time Differencing Methods for Fractional Reaction -diffusion equations, March ,2021.
• B. Janssen-Kleefeld, co-advisor, (jointly with Professor Bruce Wade, University of Wisconsin, Milwaukee): An Efficient Exponential Time Differencing Method for Nonlinear Reaction Diffusion Problems, December, 2009.
• M. Yousuf, co-advisor (jointly with Professor Bruce Wade, University of Wisconsin, Milwaukee): Higher Order Smoothing Schemes for Parabolic equations with applications to Option Pricing, Dec. 2004.
• M. Siddique, co-advisor (jointly with Professor Bruce Wade, University of Wisconsin- Milwaukee), the thesis topic : Smoothing with Positive preserving schemes for parabolic Equations, Dec. 2002.
• Co-Supervisor (jointly with Professor Edward. H. Twizell, Brunel University England) of two students who worked on the topic Sequential and Parallel Algorithm for Time Dependent PDEs, 1990-1993.
• Supervised a Ph.D. student on the topic, Numerical Modeling of Tidal Flows in the Arabian Gulf. The student was registered as an external student at Brunel University, England, while working at Bahrain University, 1986-1993.

MS Theses Supervised

Currently two students are working on predictive analytics and machine/deep learning.

• Ronald Balint, Data Driven Deep Neural Networks for systems of Odes in Chemical Kinetics, expected graduation, Summer 2023.
• Lekha Iraloor Neelakantan, Discrete SEIR Models and their application to COVID-19, Dec. 2022 
• Ziren Chen, Piecewise SEIUR model for the spread of COVID-19, May 2021.
• Lin Feng, SEIR model combined with LSTM and GRU for the trend analysis of COVID-19, May 2021.
• Nana Boating, Meshfree Methods for Black-Scholes PDE, June 2012
• Richard Ewool, Stochastic Models in Chemical Systems, August 2011
• Wedge Fernando, PDE and Monte Carlo Approaches for pricing Asian options, May 2011
• Syed H.K. Kazmi, Numerical Methods for Option Pricing Models, May 2002. Syed Karma presented the earlier findings of his thesis at the conference, 5th Mississippi State Conference on Differential Equations & Computational Simulation, Mississippi State University, May18-19, 2001.
• Tuanjie Tong, Explicit- Implicit Methods for Reaction-Diffusion Systems, April 02 2002.
• Gilbert Shanga, Locally One Dimensional Methods for Parabolic Partial Differential Equations, October, 1998.
• Bader M. Abukhodair, A Predictor-corrector Scheme for the sine-Gordon Equations, May, 1998.
• Shahan Ahmed, A Numerical Study of Reaction-Diffusion Equations, May, 1998.
• Thurya Juma, Parallel Splitting Methods for Parabolic PDEs, May 1996.
• Jianlin Cheng, Numerical Methods for Reaction Diffusion Equations: Finite Difference and Finite Element Approaches, May 1992.
• Yun Duck Kim, Finite Element Solution of Parabolic Equations with Non- Smooth Data, July 1991.
• Xiaoli Zhao, Finite Element Methods for One Dimensional Fourth Order Time Dependent Partial Differential Equations, July 1991.
• P. A. Mulconrey, Multiderivative Methods for Hyperbolic PDEs, May 1991.

Undergraduate Research Projects

• Yuan Chen, Mortality rate Prediction using Recurrence Neural Networks, presented at Actuarial Research Conference, held at University of Illinois Urban-Champaign, August 3-6, 2022.
• Jason Wix, Computational study of Dynamic Equity Model with MATLAB, Funded by STEPMT grant, College of Basic and Applied Sciences, September 2005 - May 2006.
• Robert Greenwood, Statistical analysis for the risk management of modern portfolio theory, Funded by STEPMT grant, College of Basic and Applied Sciences, January 2006 - August 2006.

Undergraduate Capstone Projects

• David Putnam, Parallel Binomial methods for American option using MPI, May 2004.
• Will J. Middlecamp, Convergence analysis of Binomial and Trinomial models for European options, May 2004.
• Salina Baafi, Cox Robison option pricing model with Excel, May 2004.
• M. Sameer, A Numerical Study of Black-Scholes Equation for European Option, May 2000.
• Lauren Morris, Cubic Spline Interpolation with JAVA, May 1998.

Undergraduate Honors Projects

• Wai-Tang Lee, Splitting Methods for Multidimensional Parabolic Partial Differential Equations, Dec. 1990 (Presented at The Annual Argonne Symposium for Undergraduates, Argonne National Lab, Argonne, IL)