Research and Teaching Interests
Numerical analysis, scientific computing, spectral methods for differential and integral equations, fast orthogonal polynomial transforms
Education
- B.Sc. University of Alberta
- M.Sc. University of Alberta
- Ph.D. University of Alberta
Current graduate students
- Ikaro Penha Costa (M.Sc. Thesis)
- Brock Klippenstein (M.Sc. Thesis)
- Yu Li (M.Sc. Thesis)
Former graduate students
- Emmanuel Appiah-Kubi (M.Sc. Thesis)
Select publications
- B. Klippenstein and R. M. Slevinsky, Fast associated classical orthogonal polynomial transforms, J. Comp. Appl. Math., 403: 113831, 2022.
- S. Olver, R. M. Slevinsky and A. Townsend, Fast algorithms using orthogonal polynomials, Acta Numerica, 29: 573–699, 2020.
- J. L. Aurentz and R. M. Slevinsky, On symmetrizing the ultraspherical spectral method for self-adjoint problems, J. Comp. Phys., 410: 109383, 2020.
- Y. Li and R. M. Slevinsky, Fast and accurate algorithms for the computation of spherically symmetric nonlocal diffusion operators on lattices, J. Comp. Phys., 397: 108870, 2019.
- R. M. Slevinsky, Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series, Appl. Comput. Harmon. Anal., 47: 585–606, 2019.
- R. M. Slevinsky, H. Montanelli, and Q. Du, A spectral method for nonlocal diffusion operators on the sphere, J. Comp. Phys., 372: 893–911, 2018.
- R. M. Slevinsky, On the use of Hahn’s asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev–Jacobi transform, IMA J. Numer. Anal., 38: 102–124, 2018.
- R. M. Slevinsky and S. Olver, A fast and well-conditioned spectral method for singular integral equations, J. Comp. Phys., 332: 290–315, 2017.
- P. Gaudreau, R. M. Slevinsky and H. Safouhi, The double exponential Sinc collocation method for singular Sturm-Liouville problems, J. Math. Phys., 57: 043505-1–043505-19, 2016.
- P. Gaudreau, R. M. Slevinsky and H. Safouhi, Computing energy eigenvalues of anharmonic oscillators using the double exponential Sinc collocation method, Ann. Phys., 360: 520–538, 2015.
- R. M. Slevinsky and S. Olver, On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods, SIAM J. Sci. Comput., 37: A676–A700, 2015.
- R. M. Slevinsky and H. Safouhi, Useful properties of the coefficients of the Slevinsky-Safouhi formula for differentiation, Numer. Algor., 66: 457–477, 2014.
- P. Gaudreau, R. M. Slevinsky, and H. Safouhi, An asymptotic expansion for energy eigenvalues for anharmonic oscillators, Ann. Phys., 337: 261–277, 2013.
- R. M. Slevinsky and H. Safouhi, A comparative study of numerical steepest descent, extrapolation, and sequence transformation methods in computing semi-infinite integrals, Numer. Algor., 60: 315–337, 2012.
- P. Gaudreau, R. M. Slevinsky, and H. Safouhi, Computation of tail probabilities via extrapolation methods and connection with rational and Padé approximants, SIAM J. Sci. Comput., 34: B65–B85, 2012.
- R. M. Slevinsky and H. Safouhi, A recursive algorithm for the G transformation and accurate computation of incomplete Bessel functions, Appl. Num. Math., 60: 1411–1417, 2010.
- R. M. Slevinsky, T. Temga, M. Mouattamid, and H. Safouhi, One- and two-center ETF-integrals of first order in relativistic calculation of NMR parameters, J. Phys. A: Math. Theor., 43: 225202, 2010.
- R. M. Slevinsky and H. Safouhi, New formulae for higher order derivatives and applications, J. Comp. Appl. Math., 233: 405–419, 2009.
- R. M. Slevinsky and H. Safouhi, The S and G transformations for computing three-center nuclear attraction integrals, Int. J. Quant. Chem., 109: 1741–1747, 2009.
- M. Slevinsky and H. Safouhi, Numerical treatment of a twisted tail using extrapolation methods, Numer. Algor., 48: 301–316, 2008.
Courses taught
- MATH 1700 Calculus 2
- MATH 2130 Engineering Mathematical Analysis
- MATH 2160 Numerical Analysis 1
- MATH 3420 Numerical Analysis 2
- MATH 4330/7330 Fundamentals of Approximation Theory
- MATH 4440/7440 Numerical Analysis of Partial Differential Equations
- MATH 4910/8410 Approximation Theory and Approximation Practice
- MATH 8140 Advanced Numerical Analysis of Differential and Integral Equations