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…