Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
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 o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2023-10-01
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| Series: | Baghdad Science Journal |
| Subjects: | |
| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7543 |
| Summary: | 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.
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| ISSN: | 2078-8665 2411-7986 |