Dr. Denys Dutykh

Associate Professor · Associate Dean of Graduate Studies

Applied Mathematics

College of Computing and Mathematical Sciences

Khalifa University of Science and Technology, Abu Dhabi, UAE

Applied mathematician working on water waves, tsunami modeling and spectral numerical methods. Since 2024 these tools also serve general relativity: quasinormal modes of black holes and wormholes.

∇²u = ∂²u/∂t²

∫∫∫ ∇ × F · dS

λ = 2πc/ω

Recent Publications

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CComput. Appl. Math.

Comput. Appl. Math.

Error estimation for numerical approximations of ODEs via composition techniques. Part I: one-step methods

In this study, we introduce a refined method for estimating errors in numerical simulations of dynamical systems through an innovative application of composition techniques. Our approach involves a dual application: a basic one-step numerical method of order p in this part, and a class of Backward Difference Formulas (BDF) schemes in Part II (Deeb et al. 2026). This dual application uses complex coefficients, resulting in outputs in the complex plane. The method’s innovation lies in demonstrating that the real parts of these outputs correspond to approximations of the solutions with an enhanced order of p + 1 , while the imaginary parts serve as error estimates of the same order, a novel proof presented herein. The linear stability of the resulting scheme is improved over that of the basic one. The performance of the composition in computing the approximation is also compared. The results show that the proposed technique attains higher accuracy with reduced computational time relative to the basic integrators; compared with established methods of the same order it remains competitive in cost while additionally supplying a built-in error estimate, and it is most advantageous for integrators that lack a native error estimator. This dual composition technique has been rigorously applied to a variety of dynamical problems, demonstrating its efficacy in adapting the time step, particularly in situations where numerical schemes lack theoretical error estimates. Consequently, the technique has the potential to advance adaptive time-stepping strategies in numerical simulations.

A. Deeb, D. Dutykh2027

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AAnn. Phys.

Ann. Phys.

An exact Kerr-like rotating Morris–Thorne wormhole: Throat, ergoregion and equatorial shadow slice

We construct an exact Kerr-like rotating extension of the zero-redshift Morris–Thorne wormhole within a Teo-type stationary and axisymmetric ansatz. Imposing the Einstein equations for an anisotropic source comoving with zero angular momentum observers fixes the circumferential metric function to K(r) = r² + a² and reduces the frame-dragging function to a single radial quadrature. For b(r) = r₀²/r, this quadrature is evaluated in terms of incomplete elliptic integrals and normalised by the ADM angular momentum. The spacetime is asymptotically flat but has vanishing ADM mass, so the Kerr relation a = J_ADM/M_ADM is not applicable. The field equations leave the Kerr-like oblateness length a and the physical angular momentum J_ADM independent. The exact family is therefore labelled by (r₀, a, J_ADM). The relation J_ADM = a r₀ is used only to select a one-parameter slice for the numerical ergoregion and equatorial-capture illustrations, and not as a field-equation constraint. We obtain r_th = √(r₀² − a²), the reality bound |a| ⩽ r₀, and the regular range 0 ⩽ |a| < r₀. Within the canonical stationary foliation, the throat is characterised quasi-locally as the unique member S₀ of the closed two-surface family S_ℓ with vanishing mean curvature and positive area second variation. The surfaces r = r_th and ℓ = 0 are only coordinate representations of this surface. A signed throat-adapted coordinate displays two asymptotically flat ends, excludes closed timelike curves, and shows that the throat is timelike rather than a horizon. These geometrical and causal conclusions do not require J_ADM = a r₀. The supporting anisotropic stress tensor is reconstructed from the Einstein tensor and is interpreted here as an effective phenomenological source. No microscopic matter Lagrangian or realistic equation of state is claimed. We also determine the ergoregion onset. Because the full Hamilton–Jacobi equation is not separable, the optical result is only the one-dimensional equatorial capture interval, not the complete two-dimensional shadow.

M. E. Sukaiti, D. Batic, D. Dutykh2026

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PPhys. Rev. D

Phys. Rev. D

Quasinormal-mode analysis of a massive scalar field in a Schwarzschild background via the spectral method

We study the massive scalar quasinormal-mode spectral problem on a Schwarzschild background using an extended Chebyshev spectral method. The massive dispersion relation has a two-sheeted analytic structure, which we uniformize before discretization. This converts the radial problem into a seventh-degree polynomial eigenvalue problem while incorporating the quasinormal-mode boundary conditions at the horizon and spatial infinity. The method yields stable spectra for low multipoles, high overtones, and frequencies on both sides of the nominal mass threshold, including regimes in which Wentzel-Kramers-Brillouin and continued-fraction approaches become difficult to apply. For complex frequencies, the far-field behavior cannot be classified from the real part of the frequency alone, but depends on the complex wave number and its Riemann sheet. We also identify stable families of purely imaginary roots with approximately uniform spacing in their damping rates, whose physical interpretation remains open. The Schwarzschild scalar problem is intended as a controlled benchmark for massive-field quasinormal-mode calculations rather than as a direct model of tensorial Kerr ringdown.

D. Batic, A. Chrysostomou, A.S. Cornell, D. Dutykh2026

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Latest Blog Posts

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Turbulence resolving into a lattice of verified steps.

research

Interim Guidance on the Use of AI Tools in Postgraduate Studies and Research

Interim guidance sent to the postgraduate students of our College on using AI tools in coursework, research and the thesis, written in the week of the Navier–Stokes announcement.

September 13, 202620 min read

Table 1: the Cayley–Dickson staircase from the reals to the sedenions, listing the property surrendered at each doubling of the dimension.

mathematics

The Cayley–Dickson Staircase: What Each Doubling Costs

The Cayley–Dickson staircase is usually presented as far as the octonions. One step further, at the sedenions of real dimension 16, alternativity, division and the multiplicative norm all fall at once.

November 16, 20251 min read

The de Bruijn–Springer theorem: the convex weights expressing the critical points in terms of the roots can be chosen with column sums equal to 1 - 1/n.

mathematics

From Gauss–Lucas to de Bruijn–Springer

Gauss–Lucas puts the roots of the derivative inside the convex hull of the roots. De Bruijn and Springer conjectured in 1948 that they are pulled inward on average — it took 55 years and two proofs.

November 2, 20252 min read

dds@spy

Cloning into 'academic-web-genesis'...
✔ Receiving objects: 100% (842/842), done.
Switched to a new branch 'feature/terminal-component'
[feature/terminal-component 7fa91b3] feat: add interactive terminal component3 files changed, 125 insertions(+)
✔ Branch 'feature/terminal-component' set up to track remote branch.
ℹ Create a pull request for 'feature/terminal-component' on GitHub:https://github.com/dutykh/academic-web-genesis/pull/new
✔ Packages installed successfullyDependencies: 57, devDependencies: 28
▲ Next.js 15.3.4 (Turbopack)- Local: http://localhost:3000✓ Ready in 875ms

Dr. Denys Dutykh

Associate Professor of Applied Mathematics

Always learning, always building.

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