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Jacobi collocation method for numerical solution of nonlinear weakly singular Volterra integro-differential equations: fractional and stochastic cases | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 مهر 1403 اصل مقاله (1.26 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2024.63023.2800 | ||
| نویسندگان | ||
| Qassim Hadi Haddam؛ Esmaeil Najafi* ؛ Saeed Sohrabi | ||
| Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran. | ||
| چکیده | ||
| This paper deals with the numerical solution of a class of nonlinear multi-term weakly singular fractional Volterra integro-differential equations by Jacobi collocation method based on the orthogonal polynomials. Since the solution of the proposed equation is not smooth enough in the origin, thus the idea of the smoothing transformation is used on the equation to incearse the smoothness of the solution. We represent an operator-based discussion of smoothing transformation and Gauss-Jacobi quadrature for Riemann-Liouville integral op- erators and weakly singular integral operators using their similar constructions and extend it to the error analysis of the proposed method and obtain an error bound for the discrete collocation solution. In addition, we propose an improved stochastic method, based on the efficient sum-of-exponentials (SOE) approximation, to address the low computational efficiency of the proposed method. To test the efficiency and accuracy, various numerical ex- amples are solved by the proposed method and the obtained error results are in accordance with the convergence analysis of the method. Finally we brought an example regarding the stochastic Volterra integro-differential equations of one singular kernel function. | ||
| کلیدواژه‌ها | ||
| Fractional calculus؛ multi-term Volterra integro-differential equations؛ Smoothing transformation؛ SOE approximation؛ Stochastic | ||
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آمار تعداد مشاهده مقاله: 39 تعداد دریافت فایل اصل مقاله: 123 |
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