Mathematics

Research Interests

High Order Numerical Methods for Partial Differential Equations: Pseudospectral and Radial Basis Function methods
Approximation Theory: Spectral Postprocessing, Orthogonal Polynomials, Radial Basis Functions, Wavelets, etc.
Mathematical Software and Scientific Computing
Mathematics Education: Development of interactive software for use in teaching and learning Mathematics

Journal Publications

Spectral Methods with Postprocessing for Numerical Hyperbolic Heat Transfer. Numerical Heat Transfer, Part A, vol. 43 no. 7 (2003), p. 717-730.
Chebyshev Super Spectral Viscosity method for a Fluidized Bed Model. Journal of Computational Physics, 186/2, p. 630-651 (2003).
Chebyshev Super Spectral Viscosity method for a Two-Dimensional Fluidized Bed Model. International Journal of Numerical Methods in Fluids, vol. 42, p. 249-263.
The Spectral Signal Processing Suite. ACM Transactions on Mathematical Software, vol. 29, no. 2, June 2003, p. 1-23.
The Method of Characteristics with applications to Conservation Laws. Journal of Online Mathematics and Applications (JOMA), Volume 3, February 2003. [applet]
Adaptive Radial Basis Function Methods for time dependent Partial Differential Equations. Applied Numerical Mathematics, vol. 54, issue 1, p. 79-94, June 2005.
Integrated Multiquadric Radial Basis Function Approximation Methods. Computers and Mathematics with Applications, vol. 51, no. 8, April 2006, p. 1283-1296.
Digital Total Variation Filtering as Postprocessing for Pseudospectral Methods for Conservation Laws. Numerical Algorithms, vol. 41, p. 17-33, 2006.
Digital Total Variation Filtering as postprocessing for Radial Basis Function Approximation Methods. Computers and Mathematics with Applications, vol. 52, p. 1119-1130, Sept. 2006.
Chebyshev Interpolation: an interactive tour. Journal of Online Mathematics and Applications, September 2006.
A Numerical Study of the Accuracy and Stability of Symmetric and Asymmetric RBF Collocation methods for Hyperbolic PDEs. Numerical Methods for Partial Differential Equations, vol. 24, no. 2, p. 670 - 686, 2008.
A Pseudospectral Method with Edge Detection Free Postprocessing for 2d Hyperbolic Heat Transfer. Numerical Heat Transfer, Part B: Fundamentals, vol. 54, no. 1, 2008, p. 52-61.
Edge Detection Free Postprocessing for Pseudospectral Approximations. Journal of Scientific Computing, vol. 51, no. 1, p. 49-61, 2009.
A Random Variable Shape Parameter Strategy for Radial Basis Function Approximation Methods (with D. Sturgill). Engineering Analysis with Boundary Elements, vol. 33, p. 1239-1245, 2009.
Multiquadric Radial Basis Function Approximation Methods for the Numerical Solution of Partial Differential Equations (with E. J. Kansa). Advances in Computational Mechanics, volume 2, 2009. ISSN: 1940-5820. (Matlab m-files, pdf).
Algorithm 899: The Matlab Postprocessing Toolkit. ACM Transactions on Mathematical Software, vol. 37, no. 1, 2010.
Radial Basis Function approximation methods with extended precision floating point arithmetic. Engineering Analysis with Boundary Elements, Volume 35, Issue 1, January 2011, Pages 68-76.
A Linear System-Free Gaussian RBF Method for the Gross-Pitaevskii equation on unbounded domains. To appear in Numerical Methods for Partial Differential Equations, 2011.
Stability properties of a predictor-corrector implementation of an implicit linear multistep method (with C. Meador). Involve, vol. 4, no. 1, p. 43-51, 2011.
On the numerical solution of chaotic dynamical systems using extend precision floating point arithmetic and very high order numerical methods (with C. Meador). Nonlinear Analysis: Modelling and Control, vol. 16, no. 3, 2011, p. 340-352.

Bibtex entries for publications above.

Technical Reports

A numerical study of a technique for shifting eigenvalues of radial basis function differentiation matrices (with A. Heryudono and C. Wang). MU-MTH-TR-2011-1.

Classes

Previously at West Virginia University: College Algebra (Math 126), Calculus 1 (Math 155), Calculus 2 (Math 156), Calculus 3 (Math 251), Differential Equations (Math 261)
Previously at Marshall University: Honors College Algebra (MTH 130), Numerical Analysis (MTH 443/643), Calculus 1 (MTH 229), Calculus 2 (MTH 230), Selected Topics in College Algebra (MTH 123), Numerical Partial Differential Equations (MTH 667), Concepts and Applications of Mathematics (MTH 121), Numerical Linear Algebra (MTH 442/642), Differential Equations (MTH 335), Problem Solving in Scientific Computing (HON 396), Mathematical Biology Seminar (MTH/BSC 280)
Fall 2011: Numerical Analysis (MTH 443/643)
Spring 2012: Mathematical Biology Seminar (MTH/BSC 280)