Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
DOI:
https://doi.org/10.21123/bsj.2023.7543Keywords:
Non-linear Sturm-Liouville problems, Newton-Kantorovich method, Finite Difference Method, Adomian’s decomposition methodAbstract
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.
Received 12/6/2022
Revised 20/8/2022
Accepted 21/8/2022
Published Online First 20/3/2023
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