Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
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Published:2023-03-20
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Volume:
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ISSN:2411-7986
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Container-title:Baghdad Science Journal
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language:
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Short-container-title:Baghdad Sci.J
Author:
Abugirda Hussien A. H.ORCID,
Al-Yasiri Khaldoun S.ORCID,
Abdullah Mohammed Kh.ORCID
Abstract
Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’ knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by applying the well-known Newton-Kantorovich method. Also, to show the efficiency of applying this method to solve these problems, a comparison is made in this paper between the Newton-Kantorovich method and the Adomian decomposition method applied to the same non-linear Sturm-Liouville problems under consideration in this work. As a result of this comparison, the results of the Newton-Kantorovich method agreed with the results obtained by applying Adomian’s decomposition method.
Publisher
College of Science for Women
Subject
General Physics and Astronomy,Agricultural and Biological Sciences (miscellaneous),General Biochemistry, Genetics and Molecular Biology,General Mathematics,General Chemistry,General Computer Science