Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences
https://hdl.handle.net/20.500.12573/45
2023-03-22T15:35:23Z
2023-03-22T15:35:23Z
A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
Zeybek, Halil
Karakoç, Battal Gazi
https://hdl.handle.net/20.500.12573/1406
2022-11-14T06:56:01Z
2016-01-01T00:00:00Z
A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
Zeybek, Halil; Karakoç, Battal Gazi
In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.
2016-01-01T00:00:00Z
Comparative assessment of smooth and non-smooth optimization solvers in HANSO software
Tor, Ali Hakan
https://hdl.handle.net/20.500.12573/1259
2022-04-12T08:56:40Z
2021-01-01T00:00:00Z
Comparative assessment of smooth and non-smooth optimization solvers in HANSO software
Tor, Ali Hakan
The aim of this study is to compare the performance of smooth and nonsmooth optimization solvers from HANSO (Hybrid Algorithm for Nonsmooth Optimization) software. The smooth optimization solver is the implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and the nonsmooth optimization solver is the Hybrid Algorithm for Nonsmooth Optimization. More precisely, the nonsmooth optimization algorithm is the combination of the BFGS and the Gradient Sampling Algorithm (GSA). We use well-known collection of academic test problems for nonsmooth optimization containing both convex and nonconvex problems. The motivation for this research is the importance of the comparative assessment of smooth optimization methods for solving nonsmooth optimization problems. This assessment will demonstrate how successful is the BFGS method for solving nonsmooth optimization problems in comparison with the nonsmooth optimization solver from HANSO. Performance profiles using the number iterations, the number of function evaluations and the number of subgradient evaluations are used to compare solvers. © 2021 Balikesir University. All rights reserved.
2021-01-01T00:00:00Z
A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis
Aydogmus, Ozgur
Tor, Ali Hakan
https://hdl.handle.net/20.500.12573/1119
2022-07-29T14:20:43Z
2021-01-01T00:00:00Z
A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis
Aydogmus, Ozgur; Tor, Ali Hakan
To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous computational cost. The method of multiple shooting, on the other hand, takes its place in between these two extremes. The computational cost of the algorithm is mostly due to the calculation of directional derivatives of objective and constraint functions. Here we modify the multiple shooting algorithm to use the adjoint method in calculating these derivatives. In the literature, this method is known to be a more stable and computationally efficient way of computing gradients of scalar functions. A predator-prey system is used to show the performance of the method and supply all necessary information for a successful and efficient implementation. (C) 2020 Elsevier Inc. All rights reserved.
2021-01-01T00:00:00Z
Existence results for a class of boundary value problems for fractional differential equations
Dogan, Abdulkadir
https://hdl.handle.net/20.500.12573/1040
2021-11-27T07:58:25Z
2021-01-01T00:00:00Z
Existence results for a class of boundary value problems for fractional differential equations
Dogan, Abdulkadir
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the LeraySchauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
2021-01-01T00:00:00Z