Mathematics

Research Interests

• High Order Numerical Methods for Partial Differential Equations: Spectral Methods, Radial Basis Function Methods, Wavelet Methods, etc.
• Approximation Theory: Spectral Postprocessing, Radial Basis Functions, Wavelets, etc.
• Computational Mathematics and Scientific Computing
• Mathematics Education: Development of interactive software for use in teaching and learning Mathematics.

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.
  
• The Matlab Postprocessing Toolkit.  Submitted to ACM Transactions on Mathematical Software.   December 2007.

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 (Math 130), Numerical Analysis (Math 443/543), Calculus 1 (Math 229), Selected Topics in College Algebra (Math 123),  Numerical Partial Differential Equations (Math 667), Concepts and Applications of Mathematics (Math 121), Numerical Linear Algebra (Math 442/542), Differential Equations (Math 335), Problem Solving in Scientific Computing (HON 396), Calculus 2 (MTH 230)
• Numerical Mathematics sequence - Numerical Analysis, Numerical Partial Differential Equations, Numerical Linear Algebra
  
• Fall 2008: Numerical Analysis (MTH 443/643), Numerical Differential Equations (MTH 667), College Algebra (MTH 130)
  

*, #