Dr. Lih-Ing Wu Roeger Associate Professor Department of Mathematics and Statistics Texas Tech University Lubbock, Texas 79409-1042 Room 202, Math Building Phone: (806) 742-2580 ext 249 Fax: (806) 742-1112 E-mail: lih-ing.roeger@ttu.edu

Professional/Research

• Research papers that are submitted and under review:
  1. L.-I. Wu Roeger. Exact finite-difference method for second-order linear equations with constant coefficients.
  2. C. P. Bhunu, W. Garira, S. Mushayabasa, J. M. Tchuenche, L.-I. Wu Roeger, Tuberculosis transmission model incorporating case detection and treatment strategy.
• Research papers that are published or accepted:
  1. L.-I. Wu Roeger. Dynamically consistent finite difference schemes for the differential equation $dy/dt=b_ny^n+b_{n-1}y^{n-1}+\cdots+b_1 y+b_0$. To appear in the Journal of Difference Equations and Applications.
  2. L.-I. Wu Roeger. and R. Gelca. Dynamically consistent discrete-time Lotka-Volterra competition models. Discrete and Continuous Dynamical Systems, Dedicated to the 7th AIMS Conference, Arlington, TX. Edited by X. Hou, X. Lu, A. Miranville, J. Su, and J. Zhu. Supplement 2009: 650-658, 2009.
  3. S.-B. Hsu and L.-I. Wu Roeger. Heteroclinic cycles in the chemostat models and the winnerless competition principle. J. Math. Anal. Appl., 360: 599-608, 2009.
  4. L.-I. Wu Roeger, Z. Feng, and C. Castillo-Chavez. Modelling TB and HIV Coinfections. Mathematical Biosciences and Engineering, 6: 817-839, 2009.
  5. J. A. D. Appleby, A. Rodkina, and L.-I. Wu Roeger. Stability of a limit cycle for a planar system with stochastic perturbations. Functional Differential Equations, 16: 73-91, 2009.
  6. W. Hernandez-Padilla and L.-I. Wu Roeger. Local stability of a discrete competition model derived from a nonstandard numerical method. Advanced Studies in Pure Mathematics, ICDEA2006, 53: 295-302, 2009.
  7. L.-I. Wu Roeger. General nonstandard finite-difference schemes for differential equations with three fixed-points.  Computers and Mathematics with Applications, 57: 379-383, 2009.
  8. L.-I. Wu Roeger. Nonstandard finite difference schemes for differential equations with n+1 distinct fixed-points. Journal of Difference Equations and Applications, 15: 133-151, 2009.
  9. L.-I. Wu Roeger. Exact finite-difference schemes for two-dimensional linear systems with constant coefficients.  Journal of Computational and Applied Mathematics, 219: 102-109, 2008.
  10. L.-I. Wu Roeger. Periodic solutions preserved by nonstandard finite-difference schemes for Lotka-Volterra system: a different approach. Journal of Difference Equations and Applications, 14: 481-493, 2008.
  11. L.-I. Wu Roeger. Exact nonstandard finite-difference methods for a linear system---the case of centers. Journal of Difference Equations and Applications, 14: 381-389, 2008.
  12. L.-I. Wu Roeger. Dynamically consistent discrete Lotka-Volterra competition models derived from nonstandard finite-difference schemes. Discrete and Continuous Dynamical Systems Series B, 9: 415-429, 2008.
  13. L.-I. Wu Roeger and R. E. Mickens. Exact finite-difference schemes for first order differential equations having three fixed points. Journal of Difference Equations and Applications, 13: 1179-1185, 2007.
  14. J. M. Cushing, S. Henson, and L.-I. Wu Roeger. A competition model for species with juvenile-adult life cycle stages. Journal of Biological Dynamics, 1: 201-231, 2007.
  15. S.-B. Hsu and L.-I. Wu Roeger. The final size of a SARS epidemic model without quarantine. Journal of Mathematical Analysis and Applications, 333: 557-566, 2007.
  16. L.-I. Wu Roeger and R. W. Barnard. Preservation of local dynamics when applying central difference methods: application to SIR model. Journal of Difference Equations and Applications, 13: 333-340, 2007.
  17. L.-I. Wu Roeger. Nonstandard finite-difference schemes for the Lotka-Volterra systems: generalization of Mickens's method. Journal of Difference Equations and Applications, 12: 937-948, 2006.
  18. L.-I. Wu Roeger. Nonstandard discretization methods on Lotka-Volterra differential equations. A chapter in Advances in the Applications of Nonstandard Finite Difference Schemes, edited by Ronald E Mickens (Clark Atlanta University, USA), World Scientific, 2005.
  19. L.-I. Wu Roeger. A nonstandard discretization method for Lotka-Volterra models that preserves periodic solutions. Journal of Difference Equations and Applications, 11: 721-733, 2005.
  20. L.-I. Wu Roeger. Discrete May-Leonard competition models II. Discrete and Continuous Dynamical Systems Series B, 5: 841-860, 2005.
  21. L.-I. Wu Roeger. Hopf bifurcations in discrete May-Leonard competition models. Canadian Applied Mathematics Quarterly, 11: 175-194, 2005.
  22. L.-I. Wu Roeger. Discrete May-Leonard competition models III. Journal of Difference Equations and Applications, 10: 773-790, 2004.
  23. L.-I. Wu Roeger. Local stability of Euler's and Kahan's methods. Journal of Difference Equations and Applications, 10: 601-614, 2004.
  24. K. W. Blayneh and L.-I. Wu Roeger. Asymptotic dynamics of an age-structured host-parasitoid model. Applicable Analysis, 83: 787-798, 2004.
  25. L.-I. Wu Roeger and L. J. S. Allen. Discrete May-Leonard competition models I. Journal of Difference Equations and Applications, 10: 77-98, 2004.
  26. L.-I. Wu and Z. Feng. Homoclinic bifurcation in an SIQR model for childhood diseases. J. Diff. Equations, 168: 150-167, 2000.
  27. C.-W. Chi, S.-B. Hsu, and L.-I. Wu. On the asymmetric May-Leonard model of three competing species. SIAM J. Appl. Math., 58: 211-226, 1998.

Resources for students

• A Pretty Good Student, a poem by Charles Osgood.
• The Most Common Errors in Undergraduate Mathematics
• AMS Resources for Undergraduates in Mathematics
• Graduate Study in the Computer and Mathematical Sciences: A Survival Manual (PDF version or PostScript version)

Mathematics Sources

• Association for Women in Mathematics
• Society for Mathematical Biology
• American Mathematical Society
• Society for Industrial and Applied Mathematics
• The Mathematical Association of America
• MathSciNet