Muaz Seydaoğlu

Muaz Seydaoğlu
Mus Alparslan University · Depertmant of mathematics

PhD

About

18
Publications
1,954
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146
Citations
Citations since 2016
15 Research Items
141 Citations
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20162017201820192020202120220102030
20162017201820192020202120220102030

Publications

Publications (18)
Article
In order to approximate the solution of the one-dimensional Burgers’ equation, an accurate algorithm is developed on the combination of the barycentric collocation technique and a high-order group preserving method for space and time discretization, respectively. We have performed this algorithm on two different test examples for various values of...
Article
In this study, we investigate the numerical solution of the higher odd-order PDEs, called the Kawahara and Kawahara-KdV equations, which are main models to study the dynamics of water waves. We combine the two-stage fourth order exponential Rosenbrock integrator with a meshfree scheme based on multiquadric-radial basis function (MQ-RBF) in time and...
Article
In the present paper, two effective numerical schemes depending on a second-order Strang splitting technique are presented to obtain approximate solutions of the one-dimensional Burgers’ equation utilizing the collocation technique and approximating directly the solution by multiquadric-radial basis function (MQ-RBF) method. To show the performance...
Article
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on Chebyshev polynomials of degrees 2, 4, 8, 12 and 18 which are computed with only 1, 2, 3, 4 and 5 matrix-matrix p...
Preprint
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We present a practical algorithm to approximate the exponential of skew-Hermitian matrices based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on Chebyshev polynomials of degrees 2, 4, 8, 12 and 18 which are computed with only 1, 2, 3, 4 and 5 matrix-matrix products, respectively....
Article
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be used in single and double precision arithmetic. The resulting algorithms are more efficient than schemes base...
Preprint
Full-text available
A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be used in single and double precision arithmetic. The resulting algorithms are more efficient than schemes base...
Article
This study focuses on symplectic integrators for numerical evaluation of the asymptotic solutions of the nonlinear Airy-type equations obtained by reducing the nonlinear dispersive equations. Since the nature of Airy-type equations has both highly oscillatory slow decay and exponential fast decay, most of classical integrators are not able to corre...
Article
Full-text available
This article proposes some higher order splitting-up techniques based on the cubic B-spline Galerkin finite element method in analyzing the Burgers equation model. The strong form of both conservation and diffusion parts of the time-split Burgers equation have been considered in building the Galerkin approach.To integrate the corresponding ODE syst...
Article
Full-text available
An ordinary differential equation (ODE) can be split into simpler sub equations and each of the sub equations is solved subsequently by a numerical method. Such a procedure involves splitting error and numerical error caused by the time stepping methods applied to sub equations. The aim of the paper is to present an integral formula for the global...
Article
We present convergence analysis of operator splitting methods applied to the nonlinear Rosenau–Burgers equation. The equation is first splitted into an unbounded linear part and a bounded nonlinear part and then operator splitting methods of Lie‐Trotter and Strang type are applied to the equation. The local error bounds are obtained by using an app...
Article
Full-text available
An efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity are made with the exact solutions and the reported r...
Article
Most of the existing numerical schemes developed to solve Burgers’ equation cannot exhibit its correct physical behavior for very small values of viscosity. This difficulty can be overcome by using splitting methods derived for near-integrable system. This class of methods has positive real coefficients and can be used for non-reversible systems su...
Article
Full-text available
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operat...
Article
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian function and the fundamental matrix solution is a symplectic matrix. This is a very important property to be...
Article
Full-text available
In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and can not be used for time-irreversible...
Article
Full-text available
We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum $A=D+\varepsilon B$ of a sparse and efficiently exponentiable matrix $D$ with sparse exponential $e^D$ and a dense matrix $\varepsilon B$ which is of small norm in comparison with $D$. The predominant algorithm is based on scali...
Article
We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coefficients of order greater than two necessarily have negative coefficients). We propose to consider a class of methods in which one set of the coefficients are real and positive num...

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