Browsing by Author "Dag, HG"

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    BOOLE COLLOCATION METHOD BASED ON RESIDUAL CORRECTION FOR SOLVING LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
    Dag, HG; Bicer, KE
    In this study, a Boole polynomial based method is presented for solving the linear Fredholm integro-differential equation approximately. In this method, the given problem is reduced to a matrix equation. The solution of the obtained matrix equation is found by using Boole polynomial, its derivatives and collocation points. This solution is obtained as the truncated Boole series which are defined in the interval [a, b]. In order to demonstrate the validity and applicability of the method, numerical examples are included. Also, the error analysis related with residual function is performed and the found approximate solutions are calculated.
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    NUMERICAL METHOD BASED ON BOOLE POLYNOMIAL FOR SOLUTION OF GENERAL FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH HYBRID DELAYS
    Biçer, KE; Dag, HG
    In this paper, the approximate solution of general functional integro differential equaions with hybrid delays is examined using of Boole polynomials and the collocation points. The solution is obtained as a truncated Boole series on a closed interval in the set of real numbers. By using this method, the approximate solutions of the problems are found. In addition, the error functions of the solutions are calculated by using the residual functions. Furthermore, the fundamental properties of the Boole polynomials and their generating functions are studied. Relationships between Boole polynomials and numbers, Stirling numbers and Euler polynomials and numbers are presented.
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    Numerical solutions of differential equations having cubic nonlinearity using Boole collocation method
    Biçer, KE; Dag, HG
    The aim of the study is to develop a numerical method for the solution of cubic nonlinear differential equations in which the numerical solution is based on Boole polynomials. That solution is in the form of the truncated series and gives approximate solution for nonlinear equations of cubic type. In this method, firstly, the matrix form of the serial solution is set and the nonlinear differential equation is converted into a matrix equation system. By adding the effect of both the conditions of the problem and the collocation points to this system of equations, we obtain the new system of equations. The coefficients of Boole-based serial solution are obtained from the solution of the resulting system of equations. The theoretical part is reinforced by considering three test problems. Numerical data for Boole solutions of test problems and absolute error functions are given in tables and figures.