Mathematics
- 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
- 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
- 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)
Undergraduate
- Caitlyn Davis-McDaniel
- A Matlab graphical user interface to illustrate iterative methods for
solving nonlinear equations
- Amy Sietz -
RBF methods and Bose-Einstein Condensates
- Clyde Meador -
Numerical methods for Chaotic Dynamical Systems
- Maggie Chenoweth
- generalized Multiquadric Radial Basis Function interpolation
Research Group Links
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