پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 691 |
| تعداد مقالات | 10,035 |
| تعداد مشاهده مقاله | 71,039,341 |
| تعداد دریافت فایل اصل مقاله | 62,488,795 |
Generalized log orthogonal functions for solving a class of cordial Volterra integral equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 17، شماره 2، اردیبهشت 2026، صفحه 1-6 اصل مقاله (451.69 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.34597.5177 | ||
| نویسندگان | ||
| Saeideh Tayebinejad* ؛ Fakhrodin Mohammadi | ||
| Department of Mathematics, University of Hormozgan, Bandar Abbas, P. O. Box 3995, Iran | ||
| تاریخ دریافت: 10 تیر 1403، تاریخ پذیرش: 28 شهریور 1403 | ||
| چکیده | ||
| This paper deals with the numerical solution of a class cordial Volterra integral equation with the Mittag-Leffler solution. A numerical approach based on the generalized log orthogonal functions is proposed to solve this kind of Volterra integral equation. By using the generalized log orthogonal functions as a basis function, the presented numerical method can effectively approximate the solution of problems with singular behaviour. The error estimate with respect to $L^{2}-$norm is investigated. Finally, the accuracy of the method is illustrated through a numerical example. | ||
| کلیدواژهها | ||
| Cordial Volterra integral equation؛ Mittage−Leffler function؛ Generalized log orthogonal functions | ||
| مراجع | ||
|
[1] H. Brunner, Volterra Integral Equations: An Introduction to Theory and Applications, Vol. 30, Cambridge University Press, 2017. [2] S. Chen and J. Shen, Enriched spectral methods and applications to problems with weakly singular solutions, J. Sci. Comput. 77 (2018), 1468–1489. [3] S. Chen and J. Shen, An efficient and accurate numerical method for the spectral fractional Laplacian equation, J. Sci. Comput. 82 (2020), no. 1, 1–25. [4] S. Chen and J. Shen, Log orthogonal functions: approximation properties and applications, IMA J. Numer. Anal. 42 (2022), no. 1, 712–743. [5] Z. Darbenas and M. Oliver, Uniqueness of solutions for weakly degenerate cordial Volterra integral equations, J. Integral Equ. Appl. 31 (2019), no. 3, 307–327. [6] T. Diogo and G. Vainikko, Applicability of spline collocation to cordial Volterra equations, Math. Modell. Anal. 18 (2013), no. 1, 1–21. [7] H. Majidian, Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study, Bull. Iran. Math. Soc. 43 (2017), no. 5, 1245–1258. [8] P. Morin, R.H. Nochetto, and K.G. Siebert, Convergence of adaptive finite element methods, SIAM Rev. 44 (2002), no. 4, 631–658. [9] J. Shen and Y. Wang, M¨untz–Galerkin methods and applications to mixed Dirichlet–Neumann boundary Vavalue problems, SIAM J. Sci. Comput. 38 (2016), no. 4, A2357–A2381. [10] G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall Series in Automatic Computation, Englewood Cliffs, N. J: Prentice-Hall, Inc., 1973. [11] G. Vainikko, Cordial Volterra integral equations 1, Numer. Funct. Anal. Optim. 30 (2009), no. (9–10), 1145–1172. [12] G. Vainikko, Cordial Volterra integral equations 2, Numer. Funct. Anal. Optim. 31 (2010), no. 2, 191–219. [13] G. Vainikko, Spline collocation for cordial Volterra integral equations, Numer. Funct. Anal. Optim. 31 (2010), no. 3, 313–338. [14] G. Vainikko, Spline collocation-interpolation method for linear and nonlinear cordial Volterra integral equations, Numer. Funct. Anal. Optim. 32 (2010), no. 1, 83–109. [15] L.L. Wang and J. Shen, Error analysis for mapped Jacobi spectral methods, J. Sci. Comput. 24 (2005), 183–218. [16] Z.W. Yang, Second-kind linear Volterra integral equations with noncompact operators, Numer. Funct. Anal. Optim. 36 (2015), no. 1, 104–131. | ||
|
آمار تعداد مشاهده مقاله: 846 تعداد دریافت فایل اصل مقاله: 379 |
||