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ScopusNumerical analysis of evolution equations
I am interested in stability, convergence, error estimates, and approximation schemes for nonlinear evolution problems.
Academic profile
Zurab Vashakidze
Invited Lecturer · Department of Mathematics · School of Science and Technology · The University of Georgia
My research interests are mainly in numerical analysis and computational methods for differential equations, including nonlinear hyperbolic problems, time-discretization schemes, spectral approximation, and wave propagation.
About
Interests in applied mathematics and numerical methods
I am interested in numerical methods for differential equations and mathematical models arising in continuum mechanics and wave propagation. In recent work, I have been studying multi-layer time-discretization methods for nonlinear evolution problems, including Kirchhoff-type string equations and coupled hyperbolic systems related to the Timoshenko beam model.
Some of my recent publications also consider spectral approximation with Legendre polynomials, operator-based approximation techniques, and numerical aspects of wave propagation in discrete lattices. Recent papers list affiliations with The University of Georgia and the Ilia Vekua Institute of Applied Mathematics in Tbilisi.
Research
Areas of research interest
Hyperbolic PDEs & nonlinear dynamics
This includes numerical treatment of Kirchhoff-type strings, Timoshenko-type systems, and related models in mathematical physics.
Spectral & high-order methods
I am also interested in Legendre-Galerkin and polynomial approximation techniques for spatial discretization.
Wave propagation
Another area of interest is the analytical and numerical study of waves in discrete media, including finite sources in infinite triangular lattices.
Selected publications
Selected recent work
No publications match the current filters.
2026
PREPRINT
math.NA
Conservative Three-Layer Schemes for Kirchhoff-Type Equations
Felix Krumbiegel , Jemal Rogava , Andreas Rupp , Zurab Vashakidze
@misc{krumbiegel2026conservative,
author = {Krumbiegel, Felix and Rogava, Jemal and Rupp, Andreas and Vashakidze, Zurab},
title = {Conservative Three-Layer Schemes for Kirchhoff-Type Equations},
year = {2026},
eprint = {2609.27707},
archivePrefix = {arXiv},
primaryClass = {math.NA},
url = {https://arxiv.org/abs/2609.27707}
}2026
PREPRINT
math.NA
On the Approximation of the Unitary Operator Group Associated with a Rotation Matrix and Its Applications to Abstract Hyperbolic Equations
Jemal Rogava , Zurab Vashakidze
@misc{rogava2026unitary,
author = {Rogava, Jemal and Vashakidze, Zurab},
title = {On the Approximation of the Unitary Operator Group Associated with a Rotation Matrix and Its Applications to Abstract Hyperbolic Equations},
year = {2026},
eprint = {2607.21293},
archivePrefix = {arXiv},
primaryClass = {math.NA},
url = {https://arxiv.org/abs/2607.21293}
}2026
WILEY
Numerical
Methods
for Partial
Differential
Equations
On the Numerical Treatment of an Abstract Nonlinear System of Coupled Hyperbolic Equations Associated With the Timoshenko Model
Jemal Rogava , Zurab Vashakidze · Numerical Methods for Partial Differential Equations, 42(4), e70127
@article{rogava2026timoshenko,
author = {Rogava, Jemal and Vashakidze, Zurab},
title = {On the Numerical Treatment of an Abstract Nonlinear System of Coupled Hyperbolic Equations Associated With the Timoshenko Model},
journal = {Numerical Methods for Partial Differential Equations},
volume = {42},
number = {4},
pages = {e70127},
year = {2026},
doi = {10.1002/num.70127},
url = {https://doi.org/10.1002/num.70127}
}2025
DE GRUYTER
2025 · VOLUME 32NUMBER 5
Georgian
Mathematical
Journal
Propagation of Waves from Finite Sources Arranged in Line Segments within an Infinite Triangular Lattice
David Kapanadze , Zurab Vashakidze · Georgian Mathematical Journal, 32(5), 837–858
@article{kapanadze2025propagation,
author = {Kapanadze, David and Vashakidze, Zurab},
title = {Propagation of Waves from Finite Sources Arranged in Line Segments within an Infinite Triangular Lattice},
journal = {Georgian Mathematical Journal},
volume = {32},
number = {5},
pages = {837--858},
year = {2025},
doi = {10.1515/gmj-2025-2007},
url = {https://doi.org/10.1515/gmj-2025-2007}
}2024
WILEY · GAMM
ZAMM
Journal of Applied
Mathematics and
Mechanics
On Convergence of a Three-Layer Semi-Discrete Scheme for the Non-Linear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients
Jemal Rogava , Zurab Vashakidze · ZAMM – Zeitschrift für Angewandte Mathematik und Mechanik, 104, e202300608
@article{rogava2024kirchhoff,
author = {Rogava, Jemal and Vashakidze, Zurab},
title = {On Convergence of a Three-Layer Semi-Discrete Scheme for the Non-Linear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients},
journal = {ZAMM -- Zeitschrift für Angewandte Mathematik und Mechanik},
volume = {104},
number = {4},
pages = {e202300608},
year = {2024},
doi = {10.1002/zamm.202300608},
url = {https://doi.org/10.1002/zamm.202300608}
}2023
ELSEVIER
Journal of
MathematicalAnalysis
and Applications
On Stability and Convergence of a Three-Layer Semi-Discrete Scheme for an Abstract Analogue of the Ball Integro-Differential Equation
Jemal Rogava , Mikheil Tsiklauri, Zurab Vashakidze · Journal of Mathematical Analysis and Applications, 518(1), 126664
@article{rogava2023ball,
author = {Rogava, Jemal and Tsiklauri, Mikheil and Vashakidze, Zurab},
title = {On Stability and Convergence of a Three-Layer Semi-Discrete Scheme for an Abstract Analogue of the Ball Integro-Differential Equation},
journal = {Journal of Mathematical Analysis and Applications},
volume = {518},
number = {1},
pages = {126664},
year = {2023},
doi = {10.1016/j.jmaa.2022.126664},
url = {https://doi.org/10.1016/j.jmaa.2022.126664}
}2022
DE GRUYTER
2022 · VOLUME 29NUMBER 4
Georgian
Mathematical
Journal
On the convergence of a three-layer semi-discrete scheme for the nonlinear dynamic Kirchhoff string equation
Zurab Vashakidze · Georgian Mathematical Journal, 29(4), 615–627
@article{vashakidze2022kirchhoff,
author = {Vashakidze, Zurab},
title = {On the convergence of a three-layer semi-discrete scheme for the nonlinear dynamic Kirchhoff string equation},
journal = {Georgian Mathematical Journal},
volume = {29},
number = {4},
pages = {615--627},
year = {2022},
doi = {10.1515/gmj-2022-2149},
url = {https://doi.org/10.1515/gmj-2022-2149}
}2020
MEMOIRS
Differential
Equations and
Mathematical
Physics
Volume 79
2020
ISSN 1512-0015
An Application of the Legendre Polynomials for the Numerical Solution of the Nonlinear Dynamical Kirchhoff String Equation
Zurab Vashakidze · Memoirs on Differential Equations and Mathematical Physics, 79, 107–119
@article{vashakidze2020legendre,
author = {Vashakidze, Zurab},
title = {An Application of the Legendre Polynomials for the Numerical Solution of the Nonlinear Dynamical Kirchhoff String Equation},
journal = {Memoirs on Differential Equations and Mathematical Physics},
volume = {79},
pages = {107--119},
year = {2020},
issn = {1512-0015},
url = {https://rmi.tsu.ge/memoirs/vol79/vol79-7.pdf}
}Teaching
Courses taught at The University of Georgia
Recent courses listed on the university profile, including records for the 2024/2025 and 2025/2026 academic years.
Calculus I
Calculus II
Precalculus
Numerical Methods
Software Packages in Mathematics (MATLAB)
Theory of Functions of Complex Variables
Academic profiles
Research identifiers & external profiles
Contact
Research and academic correspondence
Please feel free to reach out if you have any questions or concerns. My institutional email addresses are shown in an obfuscated form to reduce automated harvesting. To copy an address in its standard format, use the corresponding button.
The University of Georgia
z[dot]vashakidze[at]ug[dot]edu[dot]ge
Ivane Javakhishvili Tbilisi State University
zurab[dot]vashakidze[at]tsu[dot]ge