Abstract
The Green’s function method is a powerful technique to investigate the existence and uniqueness of the solution for two-point boundary value problems. The main task of this paper is to establish the maximal order of convergence of the Green’s function method applied in the approximation of the solution for third- and fourth-order two-point boundary value problems with deviating argument. The developed iterative method uses a complete cubic spline interpolation procedure being able to provide both discrete and continuous approximation of the solution. Some numerical examples confirm the obtained theoretical results and illustrate the accuracy of the algorithm.
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Acknowledgements
The authors want to thank to anonymous reviewers for their valuable suggestions that improved the quality of this paper. The research of the first author was developed under the auspices of the institutional project No. 126/25.06.2021 sustained by University of Oradea.
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Communicated by Zhaosheng Feng.
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Bica, A.M., Curila, D. The convergence properties of the Green’s function method for third order functional differential equations. Comp. Appl. Math. 41, 352 (2022). https://doi.org/10.1007/s40314-022-02065-0
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DOI: https://doi.org/10.1007/s40314-022-02065-0
Keywords
- Third-order two-point boundary value problems
- Functional differential equations
- Green’s function method
- Complete cubic splines