# Haiyan Tian

#### Professor

**Director of the USM Summer Mathematics Institute**

**Education**

Ph.D., Applied Mathematics, University of Louisiana at Lafayette, 2002.

**Research Interests**

Nonlinear Ordinary and Partial Differential Equations

Applied Analysis

Computational Mathematics, including Numerical Analysis

Mathematical Modeling

**Recent Refereed Journal Publications**

Each Impact Factor listed below is the average of Impact Factors over 5 years 2011-2015.

1. C. Jones and H.Y. Tian, A time integration method of approximate fundamental solutions for nonlinear Poisson-type boundary value problems, Communications in Mathematical Sciences, in press.

Impact Factor: 1.332, ARC ranking: A

2. H.Y. Tian and A. Grunewald, A Delta-shaped basis method for ill-posed nonhomogeneous elliptic boundary value problems, Neural, Parallel, and Scientific Computations, 25 (2017), 1-18.

Ranked “Reputable” by National University of Singapore

3. H.Y. Tian, J. Ding and Noah H. Rhee, Approximations of Frobenius-Perron operators via piecewise quadratic functions, Dynamic Systems and Applications, 25 (2016), 557-574.

Impact Factor: 0.344, ARC ranking: B

4. J. Ding and H.Y. Tian, Solving the Yang-Baxter-like matrix equation for elementary matrices, Computers & Mathematics with Applications, 72 (2016), 1541-1548.

Impact Factor: 1.873, ARC ranking: A

5. B. Khatri Ghimire, H.Y. Tian and A.R. Lamichhane, Numerical solutions of elliptic partial differential equations using Chebyshev polynomials, Computers & Mathematics with Applications, 72 (2016), 1042-1054.

Impact Factor: 1.873, ARC ranking: A

6. H.Y. Tian, All solutions of the Yang-Baxter-like matrix equation for rank-one matrices, Applied Mathematics Letters, 51 (2016), 55-59.

Impact Factor: 1.358, ARC ranking: B

7. H.Y. Tian, H.M. Chi and C.Y. Zhao, Comparing two types of bases for solving elliptic boundary value problems, Neural, Parallel, and Scientific Computations, 23 (2015), 411-420.

Ranked “Reputable” by National University of Singapore

8. X. Zhang, H.Y. Tian and W. Chen, Local method of approximate particular solutions for two-dimensional unsteady Burgers’ equations, Computers & Mathematics with Applications, 66 (2014), 2425-2432.

Impact Factor: 1.873, ARC ranking: A

9. X. Zhang, H.Y. Tian, L. Kuo and W. Chen, A contact SPH method with high-order limiters for simulation of inviscid compressible flows, Communications in Computational Physics, 14(2) (2013), 425-442.

Impact Factor: 1.752

10. H.Q. Zhu, H.Y. Tian and Z.M. Zhang, Convergence analysis of the LDG method for singularly perturbed two-point boundary value problems, Communications in Mathematical Sciences, 9(4) (2011), 1013-1032.

Impact Factor: 1.332, ARC ranking: A

**Classes Taught at USM**

MAT 103: Trigonometry

MAT 167: Calculus I with Analytic Geometry

MAT 167H: Honors Calculus I with Analytic Geometry

MAT 168: Calculus II with Analytic Geometry

MAT 285: Introduction to Differential Equations I

MAT 305: Mathematical Commutating

MAT 326: Linear Algebra I

MAT 340: Discrete Mathematics

MAT 605: Ordinary Differential Equations

MAT 606: Partial Differential Equations

MAT 610: Numerical Linear Algebra

**Students Directed**

Corey Jones, Ph.D., May 2015

Brandon Hollingsworth, BS, May 2015

Amber Sumner Robertson, BS, May 2013

Jaeyoun Oh, MS, May 2012

Megan Richardson, MS, August 2011

Rickyta Mallett, BS, (AGEM-SREU), July 2011

Christopher Mills, BS, May 2009

Andreas Grunewald, MS, September 2008