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Spectral Collocation-Based Procedure with Shifted Third-Kind Chebyshev Polynomials for Nonlinear Time-Fractional Integro-Differential Equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 05 شهریور 1405 اصل مقاله (2.68 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70642.3524 | ||
| نویسندگان | ||
| Aml Kamal Abd El-Latief1؛ Shahenda Mohamed Sayed2؛ Emad Mohamed Abo El-Dahab2؛ Mohamed Abd El-Aziz2؛ Youssri Hassan Youssri* 3 | ||
| 1Department of Mathematics, Faculty of Science, Capital University, Helwan, Cairo 11795, Egypt. | ||
| 2Department of Mathematics, Faculty of Science, Helwan National University, Cairo 11795, Egypt. | ||
| 3Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt. | ||
| چکیده | ||
| In our study, we present a new algorithm for solving nonlinear time-fractional partial integro-differential equations \textit{(NLTFPIDEs)} with weakly singular kernels using modified shifted Chebyshev polynomials of the third kind \textit{(MSCP3K)} as basis functions. We then employ the collocation method to transform the \textit{NLTFPIDEs} into a system of equations that can be solved with appropriate algebraic techniques to obtain the unknowns. We obtain exact algebraic representations for every element of the associated matrices. These matrices have a distinct pattern that facilitates the algebraic problem and streamlines the inversion process. The novelty lies in deriving new operational matrices for MSCP3K, enabling a structured algebraic system with reduced complexity. The work advances our understanding of the approach's reliability by carefully analyzing convergence and error behavior. The suggested technique's accuracy, efficiency, and applicability are illustrated by numerical examples, complemented by comparisons with prior studies, achieving reasonable accuracy with only a few retained modes. The results demonstrate the effectiveness of this approach in solving time-fractional partial integro-differential equations, highlighting its contribution to the field's body of knowledge. | ||
| کلیدواژه‌ها | ||
| Time-fractional partial integro-differential equations؛ collocation method؛ shifted ultraspherical polynomials؛ convergence analyses | ||
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آمار تعداد مشاهده مقاله: 138 تعداد دریافت فایل اصل مقاله: 153 |
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