پیوندهای مفید
آمار
| تعداد نشریات | 27 |
| تعداد شماره‌ها | 366 |
| تعداد مقالات | 3,243 |
| تعداد مشاهده مقاله | 4,753,557 |
| تعداد دریافت فایل اصل مقاله | 3,244,521 |
Reproducing kernel method for solving wiener-hopf equations of the second kind | ||
| Journal of Hyperstructures | ||
| دوره 5، شماره 1، شهریور 2016، صفحه 56-68 اصل مقاله (140.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2016.2654 | ||
| نویسندگان | ||
| Azizallah Alvandi* 1؛ Taher Lotf1؛ M. Paripour2 | ||
| 1Department of Mathematics, Hamedan Branch, Islamic Azad University , Iran | ||
| 2Department of Science, Hamedan University of Technology, Hamedan, 65156-579, Iran. | ||
| چکیده | ||
| This paper proposed a reproducing kernel method for solving Wiener-Hopf equations of the second kind. In order to eliminate the singularity of the equation, a transform is used. The advantage of this numerical method is the representation of exact solution in reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, by improving the traditional reproducing kernel method and the definition of the operator of W Hilbert space, the solutions of Wiener Hopf equation of the second kind are obtained. The approximate solution converges uniformly and rapidly to the exact solution. Numerical examples indicate that this method is efficient for solving these equations. The validity of the method is illustrated with two examples. | ||
| کلیدواژه‌ها | ||
| Reproducing kernel method؛ Wiener-Hopf equation؛ Singular integral equation | ||
| مراجع | ||
|
[1] D.B. Hunter, Some Gauss-type formulae for the evaluation of Cauchy principle values of integrals, Numer. Math. 19 (1972), 419–424. [2] D.F. Paget, D. Elliott, An algorithm for the numerical evaluation of certain Cauchy principle values of integrals, Numer. Math. 19 (1972), 373–385. [3] C. K. Lu, The approximate of Cauchy type integral by some kinds of interpolatory splines, J. Approx. Theory. 36 (1982), 197–212. [4] S. Krenk, Numerical quadrature of periodic singular integral equations, J. Inst. Math. Appl. 21 (1978), 181–187. [5] A. Pedas, E. Tamme, Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels, J. Comput. Appl. Math. 213 (2008), 111–126. [6] X. Jin, L. M. Keer, Q. Wang, A practical method for singular integral equations of the second kind, Eng. Fracture Mech. 206 (2007), 189–195. [7] J. Du, On the numerical solution for singular integral equations with Hilbert kernel, Chin. J. Numer. Math. Appl. 11 (2) (1989), 9–27. [8] Z. Chen, Y.F. Zhou, A new method for solving Hilbert type singular integral equations, Appl. Math. Comput. 218 (2011), 406–412. [9] H. Du, J.H. Shen, Reproducing kernel method of solving singular integral equation with cosecant kernel, J. Math. Anal. Appl. 348 (2008), 308–314. [10] S. Y. Kang, I. Koltracht, G. Rawitscher,Nystrom-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels, Math. Comput. 72 (242) (2003),729–756. [11] Yan Xuan, Fu-Rong Lin, Numerical methods based on rational variable substi-tution for Wiener-Hopf equation of the second kind, Appl. Math. Comput. 236 (2012), 3528–3539. [12] G.A. Chandler, I.G. Graham, The convergence of Nystrom methods for Wiener-Hopf equations, Numer. Math. 2 (52) (1988), 345–364. [13] I.G. Graham, W.R. Mendes, Nystrom-product integration for Wiener-Hopf equa-tions with applications to radiative transfer, IMA J. Numer. Anal. 9 (1989),261–284. [14] G. Mastroianni, G. Monegato, Nystrom interpolants based on zeros of Laguerre polynomials for some Wiener-Hopf equations, IMA J. Numer. Anal. 17 (1997),621–642. [15] M. G. Cui, Y. Z. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science PubInc. Hauppauge, (2009). [16] F. Z. Geng, M. G. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Appl. 327(2007), 1167–1181. [17] X.Y. Li, B.Y. Wu, A continuous method for nonlocal functional differential equa-tions with delayed or advenced arguments, Mathematical Analysis and Applica-tions, 409 (2014), 485–493. [18] X.Y. Li, B.Y. Wu, Error estimation for the reproducing kernel method to solve linear boundary value problems, Computational and Applied Mathematics, 243 (2013), 10–15. [19] F.Z. Geng, S.P. Qian, S. Li,A numerical method for singularly perturbed turning point problems with an interior layer, 255(2014), 97–105. [20] Hong Du, Minggen Cui, Representation of the exact solution and a stability analysis on the Fredholm integral equation of the first kind in reproducing kernel space, Appl. Math. Comput. 182 (2) (2006), 1608–1614. [21] M. Cui, Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science, (2008). | ||
|
آمار تعداد مشاهده مقاله: 48 تعداد دریافت فایل اصل مقاله: 50 |
||