Browsing by Author "Biçer, KE"

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    Numerical Solution of Telegraph Equation Using Bernoulli Collocation Method
    Biçer, KE; Yalçinbas, S
    Using Bernoulli collocation method, an approximate solution of the telegraph equation has been proposed. The numerical results and comparisons with the exact solution demonstrate the validity and applicability of the technique.
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    BELL POLYNOMIAL SOLUTION OF LINEAR FREDHOLM-VOLTERRA INTEGRO DIFFERENTIAL EQUATION SYSTEMS WITH
    Yildiz, G; Sezer, M; Biçer, KE
    In this study, the Bell collocation method is applied to solve system of high order linear delay Fredholm-Volterra integro differential under initial conditions. The numerical method is substantially dependent on the truncated Bell series, their derivatives, and collocation points. By using this method, solutions of the integral system are obtained from the Bell series. Additionally, the error analysis and residual functions are performed, and some examples are provided to indicate the availability and applicability of the method.
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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.