Publications

My publications include papers , theses , software/codes , and poster presentations.

Google Scholar Profile

Papers:

1. D.R. Reynolds, S. Amihere, D. Mitchell, V.T. Luan
   Efficient and flexible multirate temporal adaptivity
   Journal of Computational and Applied Mathematics , 488, 117773 (2026).
2. G.A. Tuan, D.N. Quang, N.H. Ha, V.T. Luan
   Cumulative-sensing-aware fixed-point iteration for spatial-reuse capacity estimation in two-dimensional CSMA/CA ad-hoc networks
   (submitted, 2026)
3. V.T. Luan , N.V. Hoang,
   Two-derivative exponential Runge-Kutta methods
   (submitted, 2026).
4. J.O. Ehigie, V.T. Luan
   Efficient high-order two-derivative DIRK methods with optimized phase errors
   (submitted, 2025).
5. V.T. Luan , T. Alhsmy
   Derivation of sixth-order exponential Runge–Kutta methods for stiff systems
   Applied Mathematics Letters , 153, 10936 (2024).
6. V.T. Luan , N. V. Hoang, J.O. Ehigie
   Efficient exponential methods for genetic regulatory systems
   Journal of Computational and Applied Mathematics , 436, 115424 (2024).
7. L.T. Tuyen, V.T. Luan
   A representation theorem for set-valued submartingales
   Stochastic Analysis and Applications , 1-20 (2023).
8. V.T. Luan , T. Alhsmy
   Adaptive time-stepping exponential Runge-Kutta methods for stiff PDEs
   (Preprint, to be submitted to Journal of Scientific Computing)
9. V. T. Luan , R. Chinomona, D.R. Reynolds
   Multirate exponential Rosenbrock methods
   SIAM Journal on Scientific Computing , 44 (5), A3265–A3289 (2022).
10. J.O. Ehigie, V.T. Luan , S.A. Okunugaa, X. You
    Exponentially fitted two-derivative DIRK methods for oscillatory differential equations
    Applied Mathematics and Computation , 418, 126770 (2022).
11. V.T. Luan , D.L. Michels
    Efficient exponential time integration for simulating nonlinear coupled oscillators
    Journal of Computational and Applied Mathematics , 391, 113429 (2021).
12. V.T. Luan
    Efficient exponential Runge–Kutta methods of high order: construction and implementation
    BIT Numerical Mathematics , 61, 535–560 (2021).
13. V.T. Luan , D.L. Michels
    Exponential Rosenbrock methods and their application in visual computing
    Invited chapter in book “Rosenbrock-Wanner-Type Methods: Theory and Applications”
    (Eds. T. Jax, A. Bartel, M. Ehrhardt, M. Günther, G. Steinebach), Springer (2021).
14. V.T. Luan , D.R. Reynolds, R. Chinomona
    A new class of high-order for multirate differential equations,
    SIAM Journal on Scientific Computing , 42(2), A1245–A1268 (2020).
15. V.T. Luan , J. A. Pudykiewicz, D.R. Reynolds
    Further development of efficient and accurate time integration schemes for meteorological models,
    Journal of Computational Physics , Vol. 376, 817-837 (2019).
16. D.L. Michels, V.T. Luan , M. Tokman
    A stiffly accurate integrator for elastodynamic problems,
    ACM Transactions on Graphics , Vol. 36, No. 4, Article 116 (2017).
17. V.T. Luan , M. Tokman, G. Rainwater
    Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs,
    Journal of Computational Physics , Vol. 335, 846-864 (2017).
18. V.T. Luan
    Fourth-order two-stage explicit exponential integrators for time-dependent PDEs,
    Applied Numerical Mathematics , 112, 91–103 (2017).
19. V.T. Luan , A. Ostermann
    Parallel exponential Rosenbrock methods,
    Computers and Mathematics with Applications , 71(5), 1137–1150 (2016).
20. V.T. Luan , A. Ostermann
    Stiff order conditions for exponential Runge-Kutta methods of order five,
    Modeling, Simulation and Optimization of Complex Processes- HPSC (H.G. Bock et al. eds.), 133-143 (2014).
21. V.T. Luan , A. Ostermann
    Exponential Runge-Kutta methods of high-order for parabolic problems,
    Journal of Computational and Applied Mathematics , 256, 168-179 (2014).
22. V.T. Luan , A. Ostermann
    Exponential Rosenbrock methods of order five-derivation, analysis and numerical comparisons,
    Journal of Computational and Applied Mathematics , 255, 417-431 (2014).
23. V.T. Luan , A. Ostermann
    Exponential B-series: The stiff case,
    SIAM Journal on Numerical Analysis , 51(6), 3431-3445 (2013).
24. Q.A. Dang, V.T. Luan
    Iterative method for solving a nonlinear fourth-order boundary value problem,
    Computers and Mathematics with Applications , 60(1), 112-121 (2010).
25. Q.A. Dang, V.T. Luan , D.Q. Long
    Iterative method for solving a fourth-order differential equation with nonlinear boundary condition,
    Applied Mathematical Sciences , Vol. 4, no. 70, 3467-3481 (2010).
26. Q.A. Dang, V.T. Luan
    Iterative method for solving a nonlinear fourth-order boundary value problem arising in the study of transverse vibrations of a hinged beam,
    Publishing House of Natural Science and Technology, Hanoi, pp. 383-399 (in Vietnamese) (2010).
27. V.T. Luan , Dang Q. A
    On influence aspect of parameter in scattered data approximation problems using multiquadric RBF function,
    Journal of Computer Science and Cybernetics , 25(1), 33-42 (2009).

Software/Codes:

1. Phipm_simul_iom , written in MATLAB (a C version is being developed): Simultaneously compute all linear combinations of matrix exponential or phi- functions evaluated at some scaling of a matrix A, t*A, acting on a set of input vectors. Released Fall 2017 (freely licensed) at GitHub .
2. MERK : Multirate Exponential Runge-Kutta methods for the additively split multirate problems. Released Spring 2019 (freely licensed) at GitHub .
3. MERB : Multirate Exponential Rosenbrock methods for the additively split multirate problems. Released Summer 2022 (freely licensed) at GitHub .

Theses:

1. V.T. Luan , High-order exponential integrators
   Ph.D. thesis, University of Innsbruck (2014).
2. V.T. Luan , Some methods of unitary integration and applications (in Vietnamese)
   MSc. thesis, HUS-Vietnam National University (2008).
3. V.T. Luan , Using vector methods in solving geometry problems (in Vietnamese)
   BSc. thesis, Hanoi National University of Education (2005)

Poster presentations:

1. H. Pham, V. T. Luan
   Exponential Nyström integrators for stiff and highly oscillatory problems
   NSF CompMath PI meeting, University of Utah, Salt Lake City, UT, May 8-9, 2025
2. N.V. Hoang, V. T. Luan
   Two-derivative exponential methods for stiff PDEs
   NSF CompMath PI meeting, University of Utah, Salt Lake City, UT, May 8-9, 2025
3. N.V. Hoang, V. T. Luan, J. Ehigie
   Efficient exponential methods for genetic regulatory systems ,
   NSF CompMath PI meeting, University of Washington, Seattle, UW, July 15 -16, 2024
4. A. Payne, V. T. Luan , N.V. Hoang
   Advanced time integrators for reaction-diffusion systems in pattern formation,
   Undergraduate Research Showcase, Mississippi State University, August 2, 2023.
5. R. Raderstof, V. T. Luan , N.V. Hoang
   Innovative Time Integration for Epidemiological Models ,
   Undergraduate Research Showcase, Mississippi State University, August 4, 2022.
6. V.T. Luan , M. Ritter, W. Benger and G. Ritter
   Visualization of the Solution of Advection-Diffusion-Reaction Equations Extended to 3D ,
   DK+ Computational Interdisciplinary Modelling, March 03-06, 2013, Obergurgl, Austria.
7. V.T. Luan , M. Ritter and G. Ritter
   Visualization of the Solution of Advection-Diffusion-Reaction Equations ,
   DK+ Computational Interdisciplinary Modelling, January 28 - February 1, 2012, Obergurgl, Austria.