Browsing by Author "Lukonde, AP"

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    Pell-Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays
    Demir, DD; Lukonde, AP; Kürkçü, ÖK; Sezer, M
    In this study, a Pell-Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures.
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    Pell-Lucas polynomial method for Volterra integral equations of the second kind
    Lukonde, AP; Demir, DD; Emadifar, H; Khademi, M; Azizi, H
    This paper introduces a Pell-Lucas collocation method for solving Volterra integral equations of the second kind. The proposed method employs collocation points and represents Pell-Lucas polynomials and their derivatives in matrix vector form. By utilizing this approach, Volterra integral equations are converted into a matrix equation, wherein the undetermined coefficients correspond to the Pell-Lucas coefficients. The effectiveness and efficiency of the proposed method are demonstrated through numerical examples, which yield accurate solutions. The accuracy of these solutions is further assessed using absolute and residual error analysis. Moreover, the obtained numerical results obtained via the Pell-Lucas collocation method are compared with analytical solutions in tables and figures, thus providing a comprehensive evaluation of the method's performance.