Finite difference method for solving fractional cordial Volterra integro-differential equations with Caputo derivative | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از 05 مرداد 1405 اصل مقاله (490.17 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.37393.5447 | ||
| نویسنده | ||
| Zahra Barikbin* | ||
| Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149-16818, Iran | ||
| چکیده | ||
| This study introduces, for the first time, a fractional formulation of cordial Volterra integro-differential equations and proposes an efficient numerical algorithm for their solution. The method combines a finite difference scheme of order $\mathscr{O}(\tau^{3-\alpha})$ for discretizing the Caputo fractional derivative with a composite trapezoidal rule $\mathscr{O}(\tau^{2})$ to approximate the integral term. Theoretical analysis establishes that the unified scheme achieves an overall convergence order of $\mathscr{O}(\tau^{2})$, a result rigorously confirmed through numerical experiments. The presented examples not only validate the algorithm's accuracy but also demonstrate its effectiveness in handling fractional-order systems, addressing a gap in the numerical analysis of such equations. This work provides a foundational framework for future research on fractional cordial integro-differential problems. | ||
| کلیدواژهها | ||
| Fractional cordial Volterra integro-differential equations؛ Finite difference؛ Caputo fractional derivative؛ Composite trapezoidal rule | ||
| مراجع | ||
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