This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical examples have been analyzed to demonstrate the efficacy of the new methods in comparison to the analytical method. Therefore, the numerical compression is carried out to confirm the efficiency and precision of the modified numerical methods. Significantly, the study demonstrates that the numerical outcomes of the proposed derived and modified numerical applied methods proved to be brilliant. Finally, based on the findings of the study, it could be said that the numerical outcomes of the test-problems using proposed and modified methods agree well with the analytical solutions. Hence, we can conclude that the proposed numerical methods that are derived or modified in the analytic study of this paper are quite efficient.
Abstract
Indeed, being busy with the understanding of religion is the best sort of worship that the almighty God has given each period of time a number of scholars and wise men. They receive what has been passed down to them from their great ancestors, and those who are willing to learn will learn, their students preserve their knowledge through teaching and writing. Thus, the scholars were pioneers in this field due to the value and importance of their knowledge. They have strived in learning, explaining, and writing new subjects.
One of those scholars is sheikh (Abdulrahman Al-Penjweni) who passed away 1319 AH in one of the villages of the city of Sulaimani in Iraq. He was one of the wisest scholars, a br
... Show MoreIt is noted in the title that the paper studies the viewpoint in the novel The Dog and the Long Night by the Iranian novelist Shahranoush Parsi Pour and in the novel Alibaba's Sad Night by the Iraqi novelist Abdulkhaliq Ar-Rikabi. Both are well known novelists, and about whose stories and novels many critical books, MA theses, and Ph.D. dissertations have been written. Also, some of their literary works have won prizes. Here, the researcher shed light on the concept of viewpoint, its types, and its importance in novels in general. This was done along with tackling the two viewpoints in both novels, where similarities and differences were identified. For this end, the researcher has adopted the analytic-descriptive appro
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