Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods

Year 2023, Volume: 27 Issue: 6, 1345 - 1354, 18.12.2023

Birkan Durak , Hasan Ömür Özer , Aziz Sezgin , Lütfi Emir Sakman

https://doi.org/10.16984/saufenbilder.1342645

Abstract

A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and multiple variational iteration (MVIM). A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.

Keywords

Collocation method, nonlinear differential equations, boundary value problems, approximate solution.

Thanks

The authors would like to thank Dr. Erol Uzal for his contributions.

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