Browsing by Subject "POLYNOMIAL APPROACH"

Now showing 1 - 4 of 4
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    Approximate solution of multi-pantograph equation with variable coefficients
    (ELSEVIER) Sezer, M; yalçinbas, S; Sahin, N
    This paper deals with the approximate solution of multi-pantograph equation with nonhomogenous term in terms of Taylor polynomials. The technique we have used is based on a Taylor matrix method. In addition, some numerical examples are presented to show the properties of the given method and the results are discussed. (c) 2007 Elsevier B.V. All rights reserved.
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    A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models
    (PERGAMON-ELSEVIER SCIENCE LTD) Çayan, S; Özhan, BB; Sezer, M
    A novel matrix method based on the Taylor series called Taylor-Splitting Collocation Method is presented to solve linear and nonlinear ordinary differential equations. Unlike the previous approaches, the fundamental matrix equation is reformulated using interval splitting. The residual error estimation algorithm is presented. Convergence analysis is given in a general form. Four different mechanical models are analyzed:1. Forced oscillations of a linear spring-mass model2. Forced oscillations of a nonlinear spring-mass model3. Free oscillations of a cubic nonlinear spring-dashpot-mass model 4. Forced oscillations of a damped nonlinear pendulum model Displacement-time and velocity-time dependencies are plotted for each model. Phase portraits of nonlinear models are presented. Appropriate absolute or residual error analyses are obtained for the proposed application models. The results of the new solution approach are compared with exact, numerical, and approximate solutions from previous works. Consistent results are found.
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    A compatible Hermite-Taylor matrix-collocation technique with convergence test for second-order partial integro-differential equations containing two independent variables with functional bounds
    (SPRINGER HEIDELBERG) Yalçin, E; Sezer, M
    The aim of this study is to offer a compatible numerical technique to solve second-order linear partial integro-differential equations with variable (functional) bounds, including two independent variables, under the initial and/or boundary conditions by using hybrid Hermite and Taylor series. The method converts the presented integro-differential equation to a matrix equation including the unknown Hermite coefficients. Solving this matrix equation and applying the collocation method, the approximate solution of the problem is obtained in terms of the Hermite polynomials. Also, by means of an error estimation and convergence test related to residual functions, some examples to illustrate the accuracy and efficiency of the method are fulfilled; the obtained results are scrutinized and interpreted. All numerical computations have been performed on the computer programs.
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    Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations
    (WILEY) Yüzbasi, S; Gök, E; Sezer, M
    In this study, a practical matrix method based on Laguerre polynomials is presented to solve the higher-order linear delay differential equations with constant coefficients and functional delays under the mixed conditions. Also, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity and applicability of the method. In addition, an algorithm written in Matlab is given for the method. Copyright (c) 2013 John Wiley & Sons, Ltd.