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Publications

 

 

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).

 

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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)

 

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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.

 

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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 Expontential Runge-Kutta methods for the additively split multirate problems. Released Spring 2019 (freely licensed) at GitHub.

 

3.     MERB: Multirate Expontential Rosenbrock methods for the additively split multirate problems. Released Summer 2022 (freely licensed) at GitHub.