Boubaker Collocation Method for Approximate Solutions of the Model of Pollution for a System of Lakes

Year 2024, Volume: 16 Issue: 1, 240 - 254, 30.06.2024

Şuayip Yüzbaşı Gamze Yıldırım

https://doi.org/10.47000/tjmcs.1167568

Abstract

This paper focuses on a numerical approach for the solution of the pollution problem for a system of
lakes. The pollution problem consists of three lakes with interconnecting channels and this model corresponds to a system of linear differential equations. The main purpose of this study is to present a collocation method based on the Boubaker polynomials to obtain approximate solutions of this pollution model. Firstly, the approximation solutions are assumed in the forms of the truncated series of the Boubaker polynomials. The solution forms and their derivatives are written in the matrix forms. By means of these matrix forms, the matrix operations and the collocation points, the pollution model is reduced to a system of the algebraic linear equations. In addition, the error estimation method is presented by using the residual function. The parameters in the pollution model are selected according to the datas in the literature. For the selected parameters, the applications of the presented method are made by using a code written in MATLAB. The application results are compared with the results of other methods in the literature. The effectiveness and reliability of the presented method are observed from the obtained results.

Keywords

Approximate solutions, Boubaker polynomials, collocation method, error estimation, the pollution model of lakes

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