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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PPhys. Rev. D

Phys. Rev. D

Quasinormal Modes of Gauss–Bonnet Black Holes via the Spectral Method: Scalar, Vector, and Tensor Perturbations

We present a unified study of scalar, vector, and tensor quasinormal modes (QNMs) of Schwarzschild black holes corrected by a Gauss—Bonnet (GB) term in higher dimensions. Using a high-precision Chebyshev spectral method, we map the QNM spectra across $D\in\{5,6,7,8,10,11,12,26\}$ well beyond the regime where sixth-order WKB and characteristic-integration techniques remain reliable. Across the three spin sectors, we find several robust signatures of higher-curvature dynamics: the appearance of overdamped purely imaginary modes, non-monotonic behaviour in the real parts of higher overtones, and a strong amplification of the dimensionless QNM frequencies in string-motivated dimensions. In the scalar and vector sectors, we uncover an exact isospectrality between the scalar monopole ($\ell=0$) and vector dipole ($\ell=1$) at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorisation of the corresponding Hamiltonians. In the tensor sector, we obtain the first numerical confirmation of the long-predicted instability in six dimensions; its onset is sharply captured by the Cohn—Calogero bound and leads to the mass threshold $GM\leq 158.1\,α^{3/2}$. No analogous instability is found for $D\geq 7$, and no tensor isospectrality occurs. Converting the dimensionless frequencies to physical units suggests that the amplified modes in higher dimensions may enter the sensitivity window of future space-based detectors such as DECIGO. The merged analysis provides a comprehensive benchmark for QNMs in Einstein—Gauss—Bonnet gravity and highlights the limitations of standard approximation schemes in the strong-coupling and high-overtone regimes.

D. Batic, D. Dutykh2026

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AAnn. Phys.

Ann. Phys.

Energy conditions in consistent perfect fluid cosmology

Motivated by recent work on consistent fluid couplings in $f(R, T)$ gravity, we study cosmology in the nontrivial model $f(R, T) = R + σR T$ using the Brown variational principle for a barotropic perfect fluid. For a flat FLRW universe, we cast the field equations into Einstein-like form and obtain explicit expressions for the effective energy density, pressure and equation of state (EOS) parameter. This allows us to rewrite the null, weak, strong and dominant energy conditions as simple polynomial inequalities. We show that radiation reproduces standard relativistic cosmology, whereas for dust and $σ>0$ the effective fluid acquires negative pressure and can drive accelerated expansion. In this dust case, there exists a finite window in the Hubble parameter during which the strong energy condition is violated, but the null, weak, and dominant energy conditions remain satisfied. Conversely, whenever the strong energy condition is imposed, the other conditions are automatically fulfilled. The additional viability requirement $1 + σT > 0$ further restricts the allowed Hubble range and yields an upper bound on $σ$ that still leaves a non-empty accelerating regime. Our analysis provides a transparent energy-condition study of a consistent $R\, T$ coupling in $f(R, T)$ cosmology, based on qualitative techniques.

D. Batic, C. Boehmer, D. Dutykh2026

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Latest Blog Posts

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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

mathematics

The Bochner–Martinelli Formula

Closing the cycle on the Cauchy integral formula: Bochner–Martinelli recovers a function from its boundary data, up to a term measuring the failure of holomorphicity, with one universal kernel.

October 25, 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

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Dr. Denys Dutykh

Associate Professor of Applied Mathematics

Always learning, always building.

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