Necdet BİLDİK | Celal Bayar University (original) (raw)

Papers by Necdet BİLDİK

Scientia Iranica

In this paper, we used the Picard successive iteration method and the new modified Krasnoselskii ... more In this paper, we used the Picard successive iteration method and the new modified Krasnoselskii iteration method in order to solve different types of ordinary linear differential equations having initial conditions. By applying the new modified Krasnoselskii iteration method, not only do we obtain the approximate solutions for the problem, but also establish the corresponding iterative schemes. Finally, it is shown that the accuracy of the new iteration method (called the new modified Krasnoselskii iteration method) is substantially improved by employing variable steps which adjust themselves to the solution of the differential equation.

International Journal of Applied Physics and Mathematics, 2017

Celal Bayar Universitesi Fen Bilimleri Dergisi, 2017

In this paper, the first-order ODEs which have no systematic way to find their Lie point symmetri... more In this paper, the first-order ODEs which have no systematic way to find their Lie point symmetries -unlike higher order ODEs which have systematic ways- are reconsidered. As a first step, we considered first order PDEs which correspond to these equations by introducing reduced characteristic Q that used in the Lie’s theory. Following this step, we tried to obtain solutions of the PDEs using their Lie point symmetries. But in this process, we met some difficulties, so by taking into account some assumptions we obtained the symmetries of ODEs which are in the special form, and also their solutions.

In this paper, solution of systems of delay di erential equations, with initial conditions, using... more In this paper, solution of systems of delay di erential equations, with initial conditions, using numerical methods, including the Taylor collocation method, the Lambert W function and the variational iteration method, is considered. We have endeavored to show the most appropriate method by comparing the solutions of this system of equations with di erent types of methods. All numerical computations have been performed on the computer algebraic system, Matlab.

arXiv: Classical Analysis and ODEs, 2016

A new analytic approximate technique for addressing nonlinear problems, namely the optimal pertur... more A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and performance of the method. This technique provides us to adjust the convergence regions when necessary.Comparing different methods reveals that the proposed method is highly accurate and has great potential to be a new kind of powerful analytical tool for nonlinear differential equations.

Iranian Journal of Science and Technology-Transactions of Mechanical Engineering, 2015

In this paper, the dynamical behavior of an axially moving string modeled by fractional derivativ... more In this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. The governing equation represented motion is solved by the method of multiple scales. Considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. Numerical results indicate the effects of fractional damping on stability.

In this research paper, a different semi-analytical analysis of modified magnetohydrodynamic Jeff... more In this research paper, a different semi-analytical analysis of modified magnetohydrodynamic Jeffery–Hamel flow is conducted via the newly developed technique. We use the optimal iterative perturbation method with multiple parameters to see the effects of the magnetic field and nanoparticle on the Jeffery–Hamel flow. Comparing our new approximate solutions with some earlier works proved the excellent accuracy of the newly proposed technique. Convergence analysis of the proposed method is also discussed and error estimation is given to anticipate the accuracy of higher-order approximate solutions.

Advances in Mathematics: Scientific Journal

In this study, we recover potential function and separable boundary conditions for the inverse St... more In this study, we recover potential function and separable boundary conditions for the inverse Sturm-Liouville problem in normal form by using two partial subsets of the data which consist of its one spectrum and sequence of endpoints of eigenfunctions.

Journal of Applied Mathematics and Computing

Discrete & Continuous Dynamical Systems - S

Georgian Mathematical Journal

In this paper, we implement the optimal homotopy asymptotic method to find the approximate soluti... more In this paper, we implement the optimal homotopy asymptotic method to find the approximate solutions of the Poisson–Boltzmann equation. We also use the results of the conjugate gradient method for comparison with those of the optimal homotopy asymptotic method. Our study reveals that the optimal homotopy asymptotic method gives more effective results than conjugate gradient algorithms for the considered problems.