Browsing by Author "Bicer, KE"

Now showing 1 - 5 of 5
  • No Thumbnail Available
    Item
    BOOLE COLLOCATION METHOD BASED ON RESIDUAL CORRECTION FOR SOLVING LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION
    Dag, HG; Bicer, KE
    In this study, a Boole polynomial based method is presented for solving the linear Fredholm integro-differential equation approximately. In this method, the given problem is reduced to a matrix equation. The solution of the obtained matrix equation is found by using Boole polynomial, its derivatives and collocation points. This solution is obtained as the truncated Boole series which are defined in the interval [a, b]. In order to demonstrate the validity and applicability of the method, numerical examples are included. Also, the error analysis related with residual function is performed and the found approximate solutions are calculated.
  • No Thumbnail Available
    Item
    A COMPUTATIONAL METHOD FOR SOLVING DIFFERENTIAL EQUATIONS WITH QUADRATIC NON-LINEARITY BY USING BERNOULLI POLYNOMIALS
    Bicer, KE; 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.
  • No Thumbnail Available
    Item
    Numerical Solutions for Helmholtz Equations using Bernoulli Polynomials
    Bicer, KE; 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.
  • No Thumbnail Available
    Item
    A Matrix Approach to Solving Hyperbolic Partial Differential Equations Using Bernoulli Polynomials
    Bicer, KE; 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.
  • No Thumbnail Available
    Item
    BERNOULLI MATRIX-COLLOCATION METHOD FOR SOLVING GENERAL FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH HYBRID DELAYS
    Bicer, KE; Sezer, M
    In this study, we apply a matrix method based on Bernoulli polynomials and collocation points to solve functional integro-differential equations with hybrid delays. The main problem is reduced to a system of algebraic equations by using this method. After solving this system, we have the coefficients of the approximate solution of the given problem. The accuracy and applicability of the method is illustrated by examples and error estimation technique related to residual function is developed.