Shagi-Di Shih ¬I¤ô¦a

Shagi-Di Shih ¬I¤ô¦a
Associate Professor
Office: Ross Hall 215, (307) 766-4361 (voice)
Email: sdshih@uwyo.edu
Dept. of Math.: (307) 766-4221~2 (voice), (307) 766-6838 (fax)

Postal address
Department of Mathematics
Dept. #3036
1000 E. University Ave.
Laramie, WY 82071

Education

Ph.D., University of Maryland at College Park, 1985

Publications
Other Activities

Our research interests include singular perturbation problems, partial differential equations, and asymptotic-induced numerical methods.

Many problems arising from biology, engineering, and physics are dominated by convective processes. These problems are characterized by a class of ordinary or partial differential equations in which a small positive parameter multiplies the highest derivative term. In such problems the solution changes abruptly in a small region, either near the boundary of the domain or along a curve internal to the domain, whose width tends to zero as the parameter tends to zero. Typically, such solutions are said to possess a boundary or internal layer behavior. The structure of the layer in these problems is described by finding its governing equations subject to auxiliary conditions by virtue of singular perturbation techniques, and this structure is used in designing accurate, and stable numerical methods of computing the solutions.

Current research problems include

Internal layer structure of some singularly perturbed problems.
Oscillations of relaxation and non-relaxation type.

Publications:

Johan Grasman, Ferdinand Verhulst, and Shagi-Di Shih, The Lyapunov exponents of the Van der Pol oscillator, Mathematical Methods in the Applied Sciences, 28 (2005), no. 10, 1131-1139.

Shagi-Di Shih and Shue-Sum Chow, A power series in small energy for the period of the Lotka-Volterra system, Taiwanese Journal of Mathematics, 8 (2004), no. 4, 1-23.

Johan Grasman and Shagi-Di Shih, A parabolic singular perturbation problem with internal layer, Asymptotic Analysis, 38 (2004), no. 3-4, 309-318.

Shagi-Di Shih, Computing Lyapunov exponents of some continuous-time systems, Proceedings of the Mathematics Conference at National Central University, edited by Jann-Long Chern, National Central University, Taiwan, 2004.

Shagi-Di Shih. On periodic orbits of relaxation oscillations. Taiwanese J. Math. 6 (2002), no. 2, 205-234.

Shagi-Di Shih. Angular layer of a singularly perturbed parabolic problem with corner singularity. Canad. Appl. Math. Quart. 9 (2001), no. 2, 159-188.

Shagi-Di Shih. On a class of singularly perturbed parabolic equations. Z. Angew. Math. Mech. 81 (2001), no. 5, 337-345.

Shagi-Di Shih. Nonlinear oscillations of relaxation type. Proceedings of the Mathematics Conference at Fu Jen Catholic University, edited by Chung-Tsun Shieh, Kang C. Jea, and Tsing-Jen Ho, Fu Jen Catholic University, 287-316, 2000.

Shagi-Di Shih. Nonlinear oscillations of a Lotka-Volterra system. Proceedings of the Eighth Workshop on Differential Equations, edited by Chun-Kong Law and Jhishen Tsay, National Sun Yat-sen University, 213-237, 2000.

Shagi-Di Shih and Tarek P. Mathew. Computation of the relaxation oscillation period in Lotka-Volterra systems. Natur. Resource Modeling 13 (2000), no. 3, 389-418.

Shagi-Di Shih. The period of a Lotka-Volterra system. Taiwanese J. Math. 1 (1997), no. 4, 451-470.

Shagi-Di Shih. Solution of Burgers' equation in the quarter plane and phase shift of its viscous shock. Mathematics is for Solving Problems, a Volume in Honor of Julian D. Cole on his 70th Birthday, edited by Pamela Cook, Victor Roytburd, and Marshall Tulin, SIAM, 76-85, 1996.

Shagi-Di Shih. A novel uniform expansion for a singularly perturbed parabolic problem with corner singularity. Methods Appl. Anal. 3 (1996), no. 2, 203-227.

Shagi-Di Shih. A very slowly moving viscous shock of Burgers' equation in the quarter plane. Appl. Anal. 56 (1995), no. 1-2, 1-18.

Shagi-Di Shih and Yeou-Koung Tung. Internal layers of a transient convection-diffusion problem by perturbation methods. Advances in Water Resources 18 (1995), no. 2, 111-120.

Benito Chen, Gilberto Flores, and Shagi-Di Shih. Layered solutions to a bistable reaction-diffusion equation. J. Differential Equations 117 (1995), no. 1, 217-244.

Shagi-Di Shih. A uniform solution of a parabolic problem with angular layer behavior. Appl. Anal. 53 (1994), no. 3-4, 277-291.

Benito Chen-Charpentier and Shagi-Di Shih. A singular perturbation-numerical method for solving ordinary differential equations with layers. Computational Fluid Dynamics Journal 2 (1994) no. 4, 451-462.

Shagi-Di Shih. On the smeared solutions of the first-order methods. Advances in Computer Methods for Partial Differential Equation - VII: Proceedings of the Seventh IMACS International Conference on Computer Methods for Partial Differential Equation, edited by R. Vichnevetsky, D. Knight, and G. Richter, IMACS, 677-681, 1992.

Shagi-Di Shih. On the internal layers of some singularly perturbed problems. Proceedings of the Sixth International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, edited by J.J.H. Miller, Front Range Press, Copper Mountain, Colorado, 25-26, 1992.

Benito Chen-Charpentier and Shagi-Di Shih. A numerical perturbation method for solving ordinary differential equations with internal layers. Proceedings of the Sixth International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, edited by J.J.H. Miller, Front Range Press, Copper Mountain, Colorado, 89-90, 1992.

Shagi-Di Shih. Shock layer structure of Burgers' equation. Conference on Nonlinear Analysis, edited by Fon-Che Liu and Tai-Ping Liu, World Scientific, New Jersey, 237-257, 1991.

Shagi-Di Shih. The interior layer structure for a linear parabolic problem with discontinuous Data. Proceedings of the Symposium on Asymptotic and Computational Analysis, edited by R. Wong, Marcel Dekker, Inc., New York, 685-696, 1990.

Jin-Yuan Liu, Shagi-Di Shih, and W.J. Minkowycz. Conjugate natural convection about a vertical cylindrical fin with lateral mass flux in a saturated porous medium. International Journal of Heat and Mass Transfer 30 (1987), no. 4, 623-630.

Shagi-Di Shih and R. Bruce Kellogg. Asymptotic analysis of a singular perturbation problem. SIAM J. Math. Anal. 18 (1987), no. 5, 1467-1511.

Shagi-Di Shih. Asymptotic analysis of singular perturbation problems. Proceedings of Seminar on Differential Equations, June 3-7, 1985, Hsinchu, Taiwan, Republic of China, edited by Tai-Ping Liu and Kuo-Shung Cheng, 142-157, 1985.

Other Activities

University faculty senator, library liaison.
Journal refereeing, research proposal refereeing, tenure and promotion refereeing.
Invited speaker in professional meetings.
Book review, book manuscript review.