| Autor: |
Mariam Al-Mazmumy, Maryam Ahmed Alyami, Mona Alsulami, Asrar Saleh Alsulami, Saleh S. Redhwan |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 9, Iss 11, Pp 30548-30571 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20241475?viewType=HTML |
| Popis: |
The present study introduced modifications to the standard Adomian decomposition method (ADM) by combining the Taylor series with orthogonal polynomials, such as Legendre polynomials and the first and second kinds of Chebyshev polynomials. These improvements can be applied to solve fractional differential equations with initial-value problems in the Caputo sense. The approaches are based on the use of orthogonal polynomials, which are essential components in approximation theories. The study carefully analyzed their respective absolute error differences, highlighting the computational benefits of the proposed modifications, which offer improved accuracy and require fewer computational steps. The effectiveness and accuracy of the approach were validated through numerical examples, confirming its efficiency and reliability. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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