Mathematics
- 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.
- 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.
Bibtex entries for publications above.
- 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)
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