I have been focused on the numerical and analytical methods for solving partial and ordinary differential equations and mathematical modeling.
1. Mathematical Modeling of Glassy-winged Sharpshooter Population, with V. Hrynkiv, L. Morano, A. T. Nguyen, S. Wilder, and F. Mitchell, Mathematical Biosciences and Engineering, 11(3), 2014.
2. A Series Solution to a Partial Integro-Differential Equation Arising in Viscoelasticity, with S. Xie and V. Hrynkiv, IAENG International Journal of Applied Mathematics, 43(4), pp. 172-175, 2013.
3. Two Numerical Algorithms for Solving a Partial Integro-Differential Equation with a Weakly Singular-Kernel, with S. Xie and V. Hrynkiv, Applications and Applied Mathematics: An International Journal, 7(1), pp. 133-141, 2012.
4. Evaluation of Xylem-feeding Insects (Hemiptera: Auchenorrhyncha) in Texas Vineyards: Distribution along State-wide Environmental Gradients, with L. Morano, A. Abedi and F. Mitchell, Society of Southwestern Entomologists, 35(4): 503-512, 2010.
5. An Adomian Decomposition Method for Solving Predator Prey Model Equations, with E. Deeba and S. Xie, Journal of Concrete and Applicable Mathematics, 5(4), pp. 323-329, 2007.
Numerical and analytical methods for solving partial and ordinary differential equations and mathematical modeling. The main contribution of my research is to find both analytical and also numerical solutions of various differential equations. Also, I have tried to develop mathematical models of glassy-winged sharpshooter population in Texas vineyard and consider the optimal management protocols for protecting Pierce’s Disease in Texas vineyard using the reasonable mathematical model.
I have participated in the various undergraduate research programs so that students could have opportunities for a deeper understanding of mathematical modeling of scientific phenomena.
NSF 04-546: Interdisciplinary Training for Undergraduates in Biological and Mathematical Sciences (UBM). Co-PI. Title: UBM-Institutional: Team Research Training Program in Biology and Mathematics. Amount of Award: $899,750; Length of Award: Fall 2007-Summer 2012 (5-year program).