28 citations · 213 across the 31 of their papers we have counts for
32 papers
Predicting periodic solutions of cyclic Lotka-Volterra equations with dynamic mode decomposition
Bülent Karasözen, Murat Uzunca
Cyclic Lotka-Volterra systems in form of ODEs and PDEs are solved by linearly implicit Kahan's method, that preserves the quadratic Poisson bracket, phase space volume, Hamiltonian…
Reduced order modeling for spatio-temporal pattern approximation in diffusive Lotka-Volterra equations
Bülent Karasözen, Murat Uzunca
This paper presents an efficient reduced order modeling (ROM) framework for simulating spatio-temporal pattern formation in three-species diffusive Lotka-Volterra systems. To allev…
Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems
Bülent Karasözen, Murat Uzunca
A structure-preserving splitting integrator is developed for 3D dissipative bi-Hamiltonian/Nambu systems. The integrator uses Strang splitting for conservative and dissipative part…
Linearly implicit exponential integrators for damped Hamiltonian PDEs
Murat Uzunca, Bülent Karasözen
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integr…
Reduced-order modeling for Ablowitz-Ladik equation
Murat Uzunca, Bülent Karasözen
In this paper, reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schrödinger equation (NLSE) wit…
Global energy preserving model reduction for multi-symplectic PDEs
Murat Uzunca, Bülent Karasözen, Ayhan Aydın
Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that…
Nonintrusive model order reduction for cross-diffusion systems
Bulent Karasozen, Murat Uzunca, Gulden Mulayim
In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differ…
Intrusive and non-intrusive reduced order modeling of the rotating thermal shallow water equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equat…
Energy preserving reduced-order modelling of thermal shallow water equation
Suleyman Yildiz, Murat Uzunca, Bulent Karasozen
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form wi…
Reduced order modelling of nonlinear cross-diffusion systems
Bülent Karasözen, Gülden Mülayim, Murat Uzunca +1
In this work, we present a reduced-order model for a nonlinear cross-diffusion problem from population dynamics, for the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volte…
Structure-preserving reduced-order modelling of Korteweg de Vries equation
Bulent Karasozen, Murat Uzunca, Suleyman Yildiz
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized i…
Structure-preserving Reduced Order Modeling of non-traditional Shallow Water Equation
Süleyman Yıldız, Murat Uzunca, Bülent Karasözen
An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Pois…
Structure Preserving Model Order Reduction of Shallow Water Equations
Bülent Karasözen, Süleyman Yıldız, Murat Uzunca
In this paper, we present two different approaches for constructing reduced-order models (ROMs) for the two-dimensional shallow water equation (SWE). The first one is based on the…
Adaptive Discontinuous Galerkin Finite Elements for Advective Allen-Cahn Equation
Murat Uzunca, Ayşe Sarıaydın-Filibelioğlu
We apply a space adaptive interior penalty discontinuous Galerkin method for solving advective Allen-Cahn equation with expanding and contracting velocity fields. The advective All…
Preservation of the invariants of Lotka-Volterra equations by iterated deferred correction methods
Murat Uzunca
In this paper we apply Kahan's nonstandard discretization to three dimensional Lotka-Volterra equations in bi-Hamiltonian form. The periodicity of the solutions and all polynomial…
Structure preserving reduced order modeling for gradient systems
Tuğba Akman Yıldız, Murat Uzunca, Bülent Karasözen
Minimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using f…
Energy preserving model order reduction of the nonlinear Schrödinger equation
Bülent Karasözen, Murat Uzunca
An energy preserving reduced order model is developed for two dimensional nonlinear Schrödinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE i…
Reduced Order Optimal Control of the Convective FitzHugh-Nagumo Equation
Bülent Karasözen, Murat Uzunca, Tuğba Küçükseyhan
In this paper, we compare three model order reduction methods: the proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) and dynamic mode decomposit…
Reduced-Order Modeling for Heston Stochastic Volatility Model
Sinem Kozpınar, Murat Uzunca, Bülent Karasözen
In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pri…
Energy stable model order reduction for the Allen-Cahn equation
Murat Uzunca, Bülent Karasözen
The Allen-Cahn equation is a gradient system, where the free-energy functional decreases monotonically in time. We develop an energy stable reduced order model (ROM) for a gradient…
Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements
Sinem Kozpınar, Murat Uzunca, Bülent Karasözen
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element…
Moving Mesh Discontinuous Galerkin Methods for PDEs with Traveling Waves
Murat Uzunca, Bülent Karasözen, Tuğba Küçükseyhan
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh stra…
Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation
Bülent Karasözen, Murat Uzunca, Tuğba Küçükseyhan
We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) eq…
Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation
Murat Uzunca, Bülent Karasözen, Ayşe Sarıaydın Filibelioğlu
We develop an adaptive method of time layers with a linearly implicit Rosenbrock method as time integrator and symmetric interior penalty Galerkin method for space discretization f…