Mathematics

Research Interests

Software

Journal Publications

  1. Spectral Methods with Postprocessing for Numerical Hyperbolic Heat Transfer. Numerical Heat Transfer, Part A, vol. 43 no. 7 (2003), p. 717-730. DOI: 10.1080/713838126
  2. Chebyshev Super Spectral Viscosity method for a Fluidized Bed Model.  Journal of Computational Physics, 186/2, p. 630-651 (2003). DOI: 10.1016/S0021-9991(03)00089-5
  3. Chebyshev Super Spectral Viscosity method for a Two-Dimensional Fluidized Bed Model International Journal of Numerical Methods in Fluids, vol. 42, p. 249-263. DOI: 10.1002/fld.485
  4. The Spectral Signal Processing Suite. ACM Transactions on Mathematical Software, vol. 29, no. 2, June 2003, p. 1-23. DOI: 10.1145/779359.779364
  5. The Method of Characteristics with applications to Conservation Laws.  Journal of Online Mathematics and Applications (JOMA), Volume 3, February 2003. [applet], [pdf version]
  6. Adaptive Radial Basis Function Methods for time dependent Partial Differential Equations.  Applied Numerical Mathematics, vol. 54, issue 1, p. 79-94, June 2005. DOI: 10.1016/j.apnum.2004.07.004
  7. Integrated Multiquadric Radial Basis Function Approximation Methods. Computers and Mathematics with Applications, vol. 51, no. 8, April 2006, p. 1283-1296.  DOI: 10.1016/j.camwa.2006.04.014
  8. Digital Total Variation Filtering as Postprocessing for Pseudospectral Methods for Conservation Laws.  Numerical Algorithms, vol. 41, p. 17-33, 2006. DOI: 10.1007/s11075-005-9003-5
  9. Digital Total Variation Filtering as postprocessing for Radial Basis Function Approximation Methods. Computers and Mathematics with Applications, vol. 52, p. 1119-1130, Sept. 2006. DOI: 10.1016/j.camwa.2006.02.013
  10. Chebyshev Interpolation: an interactive tour Journal of Online Mathematics and Applications, September 2006.  [html], [pdf], [applets: Chebyshev approximation, Chebyshev polynomial, Runge phenomenon, exponential filter]
  11. 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.  DOI: 10.1002/num.20290
  12. 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. DOI: 10.1080/10407790802122485
  13. Edge Detection Free Postprocessing for Pseudospectral Approximations. Journal of Scientific Computing, vol. 51, no. 1, p. 49-61, 2009. DOI: 10.1007/s10915-009-9287-z
  14. 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. DOI: 10.1016/j.enganabound.2009.07.003
  15. 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).
  16. A Numerical Study of Generalized Multiquadric Radial Basis Function Interpolation (with M. Chenoweth). SIAM Undergraduate Research Online Volume 2, Issue 2, 2009. DOI: 10.1137/09S01040X
  17. Algorithm 899: The Matlab Postprocessing Toolkit. ACM Transactions on Mathematical Software, vol. 37, no. 1, 2010. DOI: 10.1145/1644001.1644011
  18. 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.  DOI: 10.1016/j.enganabound.2010.05.011
  19. Stability propertiesof a predictor-corrector implementation of an implicit linear multistep method (with C. Meador).  Involve, vol. 4, no. 1, p. 43-51, 2011. DOI: 10.2140/involve.2011.4.43
  20. On the numerical solution of chaotic dynamical systems using extended 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.
  21. A Linear System-Free Gaussian RBF Method for the Gross-Pitaevskii equation on unbounded domains.  Numerical Methods for Partial Differential Equations, volume 28, number 2, p. 389-401, 2012.  DOI: 10.1002/num.20623
  22. A Local Radial Basis Function method for Advection-Diffusion-Reaction equations on complexly shaped domains. Applied Mathematics and Computation, volume 218, p. 9853-9865, 2012.  Matlab files. DOI: 10.1016/j.amc.2012.03.062
  23. Regularized symmetric positive definite matrix factorizations for linear systems arising from RBF interpolation and differentiation.  Engineering Analysis with Boundary Elements, volume 44, p. 76-86, July 2014.  (source code) DOI: 10.1016/j.enganabound.2014.04.019
  24. Filtered Leapfrog Time Integration with Enhanced Stability Properties (with A. Aluthge, and R. Estep). Journal of Applied Mathematics and Physics, 4, p. 1354-1370, 2016. DOI: 10.4236/jamp.2016.47145. (source code)
  25. An examination of evaluation algorithms for the RBF methods (with S. Cogar). Engineering Analysis with Boundary Elements, volume 75, p. 36-45, February 2017. DOI: 10.1016/j.enganabound.2016.11.006, (source code)
  26. The Matlab Radial Basis Function Toolkit. Journal of Open Research Software, volume 5, issue 1, page 8, 2017. (software web page) DOI: 10.5334/jors.131
  27. Radial Basis Function Methods - the case of symmetric domains. Numerical Methods for Partial Differential Equations, 2018. DOI:10.1002/num.22272
  28. A rational radial basis function method for accurately resolving discontinuities and steep gradients (with Y. Bai). Applied Numerical Mathematics 130, p. 131-142, 2018. DOI: 10.1016/j.apnum.2018.04.001
  29. A Filtered Milne-Simpson ODE method with enhanced stability properties (2022)
  30. Local Radial Basis Functios methods: comparison, improvements, and implementation (2022)
Bibtex entries for publications above, ORCID ID: 0000-0003-0989-412X, Researchgate, doi2bib

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