Browsing by Author "Isik O.R."

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    Bernstein series solution of a class of Lane-Emden type equations
    (2013) Isik O.R.; Sezer M.
    The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some priori error estimate. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n which gives a better result in any norm. Finally, the effectiveness of the method is illustrated by some numerical experiments. Numerical results are consistent with the theoretical results. © 2013 Osman Rasit Isik and Mehmet Sezer.
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    Bernstein series solution of linear second-order partial differential equations with mixed conditions
    (John Wiley and Sons Ltd, 2014) Isik O.R.; Sezer M.; Guney Z.
    The purpose of this study is to present a new collocation method for numerical solution of linear PDEs under the most general conditions. The method is given with a priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit n, which gives better result in any norm. Finally, the effectiveness of the method is illustrated in some numerical experiments. Numerical results are consistent with the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.
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    Error analysis of the Chebyshev collocation method for linear second-order partial differential equations
    (Taylor and Francis Ltd., 2015) Yuksel G.; Isik O.R.; Sezer M.
    The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which is obtained by polynomial interpolation. The residual correction procedure is modified to the problem so that the absolute error may be estimated. Finally, the effectiveness of the method is illustrated in several numerical experiments such as Laplace and Poisson equations. Numerical results are overlapped with the theoretical results. © 2014 Taylor & Francis.
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    Taylor collocation approach for delayed Lotka-Volterra predator-prey system
    (Elsevier Inc., 2015) Gokmen E.; Isik O.R.; Sezer M.
    In this study, a numerical approach is proposed to obtain approximate solutions of the system of nonlinear delay differential equations defining Lotka-Volterra prey-predator model. By using the Taylor polynomials and collocation points, this method transforms the population model into a matrix equation. The matrix equation corresponds to a system of nonlinear equations with the unknown Taylor coefficients. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results. All numerical computations have been performed on the computer algebraic system Maple 15. © 2015 Elsevier Inc. All rights reserved.