Browsing by Subject "Bessel functions of the first kind"

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    A collocation method to find solutions of linear complex differential equations in circular domains
    (2013) Yüzbaşi Ş.; Sezer M.
    In this study, we introduce a collocation approach for solving high-order linear complex differential equations in circular domain. By using collocation points defined in a circular domain and Bessel functions of the first kind, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. Proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are given to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results obtained from the examples demonstrate the efficiency and accuracy of the present work. All of the numerical computations have been computed on computer using a code written in Matlab. © 2013 Elsevier Inc. All rights reserved.
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    An improved Bessel collocation method with a residual error function to solve a class of Lane-Emden differential equations
    (2013) YüzbaşI T.; Sezer M.
    In this study, the modified Bessel collocation method is presented to obtain the approximate solutions of the linear Lane-Emden differential equations. The method is based on the improvement of the Bessel polynomial solutions with the aid of the residual error function. First, the Bessel collocation method is applied to the linear Lane-Emden differential equations and thus the Bessel polynomial solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Bessel collocation method. By summing the Bessel polynomial solutions of the original problem and the error problem, we have the improved Bessel polynomial solutions. When the exact solution of the problem is not known, the absolute errors can be approximately computed by the Bessel polynomial solution of the error problem. In addition, examples that illustrate the pertinent features of the method are presented, and the results of this investigation are discussed. © 2012 Elsevier Ltd.