Yazar "Alkan, Sertan" seçeneğine göre listele

Listeleniyor 1 - 8 / 8
  • Küçük Resim
    Öğe
    An efficient algorithm for solving fractional differential equations with boundary conditions
    (Sciendo, 2016) Alkan, Sertan; Yildirim, Kenan; Secer, Aydin
    In this paper, a sinc-collocation method is described to determine the approximate solution of fractional order boundary value problem (FBVP). The results obtained are presented as two new theorems. The fractional derivatives are defined in the Caputo sense, which is often used in fractional calculus. In order to demonstrate the efficiency and capacity of the present method, it is applied to some FBVP with variable coefficients. Obtained results are compared to exact solutions as well as Cubic Spline solutions. The comparisons can be used to conclude that sinc-collocation method is powerful and promising method for determining the approximate solutions of FBVPs in different types of scenarios.
  • Küçük Resim
    Öğe
    Fibonacci Collocation Method for Solving a Class of Nonlinear Differential Equations
    (2023) Çakmak, Musa; Alkan, Sertan
    In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.
  • Küçük Resim
    Öğe
    Fibonacci Collocation Method for Solving a Class of Nonlinear Differential Equations
    (Association of Mathematicians (MATDER), 2023) Çakmak, Musa; Alkan, Sertan
    In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature. © MatDer.
  • Küçük Resim
    Öğe
    A NEW SOLUTION METHOD FOR NONLINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS
    (Amer Inst Mathematical Sciences, 2015) Alkan, Sertan
    The aim of this paper is to obtain approximate solution of a class of nonlinear fractional Fredholm integro-differential equations by means of sinccollocation method which is not used for solving them in the literature before. The fractional derivatives are defined in the Caputo sense often used in fractional calculus. The important feature of the present study is that obtained results are stated as two new theorems. The introduced method is tested on some nonlinear problems and it seems that the method is a very efficient and powerful tool to obtain numerical solutions of nonlinear fractional integro-differential equations.
  • Küçük Resim
    Öğe
    A numerical method for solving a class of systems of nonlinear Pantograph differential equations
    (Elsevier, 2022) Cakmak, Musa; Alkan, Sertan
    In this paper, Fibonacci collocation method is firstly used for approximately solving a class of systems of nonlinear Pantograph differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using the absolute error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in the literature. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
  • [ N/A ]
    Öğe
    Pell polynomial approach for solving a class of systems of nonlinear differential equations
    (Tbilisi Centre Math Sci, 2022) Cakmak, Musa; Alkan, Sertan
    In this study, Pell polynomial approach is used for approximately solving a class of systems of nonlinear differential equations with initial conditions. The given problem is firstly expressed as a matrix-vector system via collocation points. Then the unknown coefficients of the approximate solution are obtained. Also, some test problems are given to demonstrate accuracy and effectiveness of the proposed method. Additionally, the calculated numerical values are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.
  • Küçük Resim
    Öğe
    Solving nonlinear boundary value problems by the Galerkin method with sinc functions
    (De Gruyter Poland Sp Zoo, 2015) Alkan, Sertan; Secer, Aydin
    In this paper, the sinc-Galerkin method is used for numerically solving a class of nonlinear differential equations with boundary conditions. The importance of this study is that sinc approximation of the nonlinear term is stated as a new theorem. The method introduced here is tested on some nonlinear problems and is shown to be a very efficient and powerful tool for obtaining approximate solutions of nonlinear ordinary differential equations.
  • Küçük Resim
    Öğe
    A time-delay equation: well-posedness to optimal control
    (De Gruyter Open Ltd, 2016) Yildirim, Kenan; Alkan, Sertan
    In this paper, well-posedness, controllability and optimal control for a time-delay beam equation are studied. The equation of motion is modeled as a time-delayed distributed parameter system(DPS) and includes Heaviside functions and their spatial derivatives due to the finite size of piezoelectric patch actuators used to suppress the excessive vibrations based on displacement and moment conditions. The optimal control problem is defined with the performance index including a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time and a penalty term defined as the control voltage used in the control duration. Optimal control law is obtained by using Maximum principle and hence, the optimal control problem is transformed the into a boundary-, initial and terminal value problem. The explicit solution of the control problem is obtained by eigenfunction expansions of the state and adjoint variables. Numerical results are presented to show the effectiveness and applicability of the piezoelectric control.