Ercan Çelik

The Numerical Method for Solving Differential Equations of Lane-Emden Type by Pade Approximation

Numerical solution differential equation of Lane-Emden type is considered by Pade approximation. We apply these method to two examples. First differential equation of Lane-Emden type has been converted to power series by one-dimensional differential transformation, then the numerical solution of equation was put into Pade series form. Thus, we have obtained numerical solution differential equation of Lane-Emden type.

The variational iteration method for fuzzy fractional differential equations with uncertainty

In this paper the variational iteration method is used to solve the fractional differential equations with a fuzzy initial condition. We consider a differential equation of fractional order with uncertainty and present the concept of solution. We compared the results with their exact solutions in order to demonstrate the validity and applicability of the method.

Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation

In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the conformable fractional Hermite differential equations, conformable fractional Hermite polynomials and basic properties of these polynomials.In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2 . Further, we introduce the conformable fractional Hermite differential equations, conformable fractional Hermite polynomials and basic properties of these polynomials.

The numerical solution of partial differential-algebraic equations

In this paper, a numerical solution of partial differential-algebraic equations (PDAEs) is considered by multivariate Padé approximations. We applied this method to an example. First, PDAE has been converted to power series by two-dimensional differential transformation, and then the numerical solution of the equation was put into a multivariate Padé series form. Thus, we obtained the numerical solution of PDAEs.

On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3

Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.

An Effective Tool: Numerical Solutions by Legendre Polynomials for High-order Linear Complex Differential Equations

In this paper, Legendre polynomials was used to get numerical solution of high-order linear complex differential equations in a circular domain. The solutions in the form of power series were obtained. The method was applied on three test problems. Obtained results demonstrated in tables are good agreement with the exact solutions. All of the numerical computations have been performed with a code written in Matlab software.

A Note on Optimal Control Problem Governed by Schrödinger Equation

Abstract In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.

Numerical solutions of linear differential-algebraic equation systems via Hartley series

In this paper, Hartley series are presented first. Then, the operational matrix of integration together with the product and coefficient matrices are presented. They are used to transform linear differential equation systems to a set of linear algebraic equations. Finally, numerical examples are given.

Optimal control problem for stationary quasi-optic equations

In this paper, an optimal control problem was taken up for a stationary equation of quasi optic. For the stationary equation of quasi optic, at first judgment relating to the existence and uniqueness of a boundary value problem was given. By using this judgment, the existence and uniqueness of the optimal control problem solutions were proved. Then we state a necessary condition to an optimal solution. We proved differentiability of a functional and obtained a formula for its gradient. By using this formula, the necessary condition for solvability of the problem is stated as the variational principle.