Browsing by Author "Erdem K."

Now showing 1 - 4 of 4
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    Approximate solutions of nonlinear volterra integral equation systems
    (2010) YalÇinba S.; Erdem K.
    The purpose of this study is to implement a new approximate method for solving system of nonlinear Volterra integral equations. The technique is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. © 2010 World Scientific Publishing Company.
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    Bernoulli polynomial approach to high-order linear differential-difference equations
    (2012) Erdem K.; Yalçinbaş S.
    In this paper, a Bernoulli matrix method is developed to find an approximate solution of high-order linear differential-difference equations with variable coeffcients under the mixed conditions. The solution is obtained in terms of Bernoulli polynomials. © 2012 American Institute of Physics.
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    Numerical approach of linear delay difference equations with variable coefficients in terms of Bernoulli polynomials
    (2012) Erdem K.; Yalçinbaş S.
    The aim of this study is to give a Bernoulli polynomial approximation for the solution of linear delay difference equations with variable coefficients under the mixed conditions about any point. For this purpose, Bernoulli matrix method is introduced. This method transforms linear delay difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed. Also we have discussed the accuracy of the method. © 2012 American Institute of Physics.
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    A Bernoulli polynomial approach with residual correction for solving mixed linear Fredholm integro-differential-difference equations
    (2013) Erdem K.; Yalçinbaş S.; Sezer M.
    In this study, an approximate method based on Bernoulli polynomials and collocation points has been presented to obtain the solution of higher order linear Fredholm integro-differential-difference equations with the mixed conditions. The method we have used consists of reducing the problem to a matrix equation which corresponds to a system of linear algebraic equations. The obtained matrix equation is based on the matrix forms of Bernoulli polynomials and their derivatives by means of collocations. The solutions are obtained as the truncated Bernoulli series which are defined in the interval [a,b]. To illustrate the method, it is applied to the initial and boundary values. Also error analysis and numerical examples are included to demonstrate the validity and applicability of the technique. © 2013 Copyright Taylor and Francis Group, LLC.