Browsing by Author "Dal, F"

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    On the application of Euler's method to linear integro differential equations and comparison with existing methods
    Elmaci, D; Baykus Savasaneril, N; Dal, F; Sezer, M
    In this study, a collocation method using Euler method for solving systems of linear integro-differential equations is presented. The solution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exact solutions and solutions obtained by other methods show that the proposed method is an effective and highly promising for linear integro-differential equation systems. All of numerical calculations have been made on a computer using a program written in Matlab.
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    EULER AND TAYLOR POLYNOMIALS METHOD FOR SOLVING VOLTERRA TYPE INTEGRO DIFFERENTIAL EQUATIONS WITH NONLINEAR TERMS
    Elmaci, D; Savasaneril, NB; Dal, F; Sezer, M
    In this study, the first order nonlinear Volterra type integro-differential equations are used in order to identify approximate solutions concerning Euler polynomials of a matrix method based on collocation points. This method converts the mentioned nonlinear integro-differential equation into the matrix equation with the utilization of Euler polynomials along with collocation points. The matrix equation is a system of nonlinear algebraic equations with the unknown Euler coefficients. Additionally, this approach provides analytic solutions, if the exact solutions are polynomials. Furthermore, some illustrative examples are presented with the aid of an error estimation by using the Mean-Value Theorem and residual functions. The obtained results show that the developed method is efficient and simple enough to be applied. And also, convergence of the solutions of the problems were examined. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB.