Browsing by Author "Yuksel G."
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Item A Chebyshev series approximation for linear second- order partial differential equations with complicated conditions(Gazi Universitesi, 2013) Yuksel G.; Sezer M.The purpose of this study is to present a new collocation method for the solution of second-order, linear partial differential equations (PDEs) under the most general conditions. The method has improved from Chebyshev matrix method, which has been given for solving of ordinary differential, integral and integro-differential equations. The method is based on the approximation by the truncated bivariate Chebyshev series. PDEs and conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown Chebyshev coefficients, via Chebyshev collocation points. Combining these matrix equations and then solving the system yields the Chebyshev coefficients of the solution function. Finally, the effectiveness of the method is illustrated in several numerical experiments and error analysis is performed.Item 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.Item A numerical approach for solving Volterra type functional integral equations with variable bounds and mixed delays(Elsevier B.V., 2017) Gokmen E.; Yuksel G.; Sezer M.In this paper, the Taylor collocation method has been used the integro functional equation with variable bounds. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. We have introduced the method to solve the functional integral equations with variable bounds. We have also improved error analysis for this method by using the residual function to estimate the absolute errors. To illustrate the pertinent features of the method numeric examples are presented and results are compared with the other methods. All numerical computations have been performed on the computer algebraic system Maple 15. © 2016 Elsevier B.V.