Browsing by Author "Bicer K.E."

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    A matrix approach to solving hyperbolic partial differential equations using Bernoulli polynomials
    (University of Nis, 2016) Bicer K.E.; Yalcinbas S.
    The present study considers the solutions of hyperbolic partial differential equations. For this, an approximate method based on Bernoulli polynomials is developed. This method transforms the equation into the matrix equation and the unknown of this equation is a Bernoulli coefficients matrix. To demostrate the validity and applicability of the method, an error analysis developed based on residual function. Also examples are presented to illustrate the accuracy of the method. © 2016, University of Nis. All rights reserved.
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    Numerical solutions for Helmholtz equations using Bernoulli polynomials
    (American Institute of Physics Inc., 2017) Bicer K.E.; Yalcinbas S.
    This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations. © 2017 Author(s).
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    A computational method for solving differential equations with quadratic non-linearity by using bernoulli polynomials
    (Serbian Society of Heat Transfer Engineers, 2019) Bicer K.E.; Sezer M.
    In this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. Both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds. © 2019 Society of Thermal Engineers of Serbia.