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Öğe The approximate solution of high-order linear fractional differential equations with variable coefficients in terms of generalized taylor polynomials(2011) Keskin Y.; Karao?lu O.; Servi S.; Oturanç G.In this paper, we have developed a new method called Generalized Taylor collocation method (GTCM), which is based on the Taylor collocation method, to give approximate solution of linear fractional differential equations with variable coefficients. Using the collocation points, this method transforms fractional differential equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Generalized Taylor coefficients. Generally, the method is based on computing the Generalized Taylor coefficients by means of the collocation points. This method does not require any intensive computation. Moreover, It is easy to write computer codes in any symbolic language. Hence, the proposed method can be used as effective alternative method for obtaining analytic and approximate solutions for fractional differential equations. The effectiveness of the proposed method is illustrated with some examples. The results show that the method is very effective and convenient in predicting the solutions of such problems. © Association for Scientific Research.Öğe The maple program procedures at solution systems of differential equation with Taylor collocation method(Springer New York LLC, 2014) Servi S.; Keskin Y.; Oturanç G.In this paper, a maple algorithm Taylor collocation method has been presented for numerically solving the systems of differential equation with variable coefficients under the mixed conditions. The solution is obtained in terms of Taylor polynomials. This method is based on taking the truncated Taylor series of the function in equations and then substituting their matrix forms in the given equation. Hence, the result of matrix equation can be solved and the unknown Taylor coefficients can be found approximately. The results obtained by Taylor collocation method will be compared with the results of differential transform method and Adomian decomposition method. © Springer International Publishing Switzerland 2014.Öğe Numerical solution of regularized long wave equation by reduced differential transform method(2010) Keskin Y.; Oturanc G.In this paper, a general framework of the reduced differential transform method is presented for solving the regularized long wave (RLW) equation. In this method, the solution is calculated in the form of convergent power series with easily computable components. The efficiency of the considered method is illustrated by some examples. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.
