Browsing by Subject "VOLTERRA INTEGRODIFFERENTIAL EQUATIONS"

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    A numerical approach for a nonhomogeneous differential equation with variable delays
    (SPRINGER HEIDELBERG) Özel, M; Tarakçi, M; Sezer, M
    In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown Morgan-Voyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.
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    Improved Jacobi matrix method for the numerical solution of Fredholm integro-differential-difference equations
    (SPRINGER HEIDELBERG) Bahsi, MM; Bahsi, AK; Çevik, M; Sezer, M
    This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi polynomials and using collocation points. The improved Jacobi polynomial solution is obtained by summing up the basic Jacobi polynomial solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi polynomial solution gives better results than the direct Jacobi polynomial solution, and also, than some other known methods. The advantage of this method is that Jacobi polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer polynomials and, therefore, is the comprehensive polynomial solution technique