پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 642 |
| تعداد مقالات | 9,410 |
| تعداد مشاهده مقاله | 68,134,848 |
| تعداد دریافت فایل اصل مقاله | 39,842,423 |
A new reproducing kernel method for solving the second order partial differential equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 26، دوره 14، شماره 2، اردیبهشت 2023، صفحه 327-339 اصل مقاله (4.33 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24802.2832 | ||
| نویسندگان | ||
| Mohammadreza Foroutan* ؛ Soheyla Morovvati Darabad؛ Kamal Fallahi | ||
| Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran | ||
| تاریخ دریافت: 15 مهر 1400، تاریخ بازنگری: 24 تیر 1401، تاریخ پذیرش: 16 مرداد 1401 | ||
| چکیده | ||
| In this study, a reproducing kernel Hilbert space method with the Chebyshev function is proposed for approximating solutions of a second-order linear partial differential equation under nonhomogeneous initial conditions. Based on reproducing kernel theory, reproducing kernel functions with a polynomial form will be erected in the reproducing kernel spaces spanned by the shifted Chebyshev polynomials. The exact solution is given by reproducing kernel functions in a series expansion form, the approximation solution is expressed by an n-term summation of reproducing kernel functions. This approximation converges to the exact solution of the partial differential equation when a sufficient number of terms are included. Convergence analysis of the proposed technique is theoretically investigated. This approach is successfully used for solving partial differential equations with nonhomogeneous boundary conditions. | ||
| کلیدواژه‌ها | ||
| Reproducing kernel Hilbert space method؛ shifted Chebyshev polynomials؛ Convergence analysis؛ Second order linear partial differential equation | ||
| مراجع | ||
|
[1] A. Akg¨ul and G. David, Existence of unique solutions to the telegraph equation in binary reproducing kernel Hilbert spaces, Diff. Equ. Dyn. Syst. 28 (2020), 715—744. [2] M. Cui and Y. Lin, Nonlinear Numerical Analysis in the Reproducing Kernel Space, Nova Science, New York, 2009. [3] M.R. Foroutan, R. Asadi and A. Ebadian, A reproducing kernel Hilbert space method for solving the nonlinear three point boundary value problems, Int. J. Number Model. El. 32 (2019), no. 3, 1–18. [4] M.R. Foroutan, A. Ebadian and R. Asadi, Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems, Int. J. Compute. Math. 95 (2018), no. 10, 2128–2142. [5] M.R. Foroutan, A. Ebadian and H. Rahmani Fazli, Generalized Jacobi reproducing kernel method in Hilbert spaces for solving the black-scholes option pricing problem arising in financial modeling, Math. Model. Anal. 23 (2018), no. 4, 538–553. [6] L.A. Harris, Bivariate lagrange interpolation at the Chebyshev nodes, Proc. Amer. Math. Soc. 138 (2010), no. 12, 4447–4453. [7] Y. Huanmin and C. Minggen, A new algorithm for a class of singular boundary value problems, Appl. Math. Comput. 186 (2007), no. 2, 1183–1191. [8] M. Khaleghi, E. Babolian and S. Abbasbandy, Chebyshev reproducing kernel method: application to two-point boundary value problems, Adv. Differ. Equ. 1 (2017), 26–39. [9] M. Khaleghi, M.T. Moghaddam, E. Babolian and S. Abbasbandy, Solving a class of singular two-point boundary value problems using new effective reproducing kernel technique, Appl. Math. Comput. 331 (2018), 264–273. [10] X.Li. and B. Wu., A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations, J. Comput. Appl. Math. 311 (2017) 387-393. [11] L.C. Mei, Y.T. Jia and Y.Z. Lin, Simplified reproducing kernel method for impulsive delay differential equations, Appl. Math. Lett. 83 (2018), 123–129. [12] C. Minggen and G. Fazhan, Solving singular two point boundary value problems in reproducing kernel space, J. Comput. Appl. Math. 205 (2007), no. 1, 4–15. [13] J. Niu, L.X. Sun and M.Q. Xu, A reproducing kernel method for solving heat conduction equations with delay, Appl. Math. Lett. 100 (2020), 106036, 7. [14] S. Saitoh and Y. Sawano, Theory of reproducing kernels and applications, Springer, 2016. [15] F. Toutounian and E. Tohidi,A new Bernolli matrix method for solving second order linear partial differential equations with the convergence analysis, Appl. Math. Comput. 223 (2013) 298-310. [16] Y. Xu, Common zeros of polynomials in several variables and higher dimensional quadrature, Pitman Research Notes in Mathematics Series. Longman, Essex, 1994. [17] M.Q. Xu and Y.Z. Lin, Simplified reproducing kernel method for fractional differential equations with delay, Appl. Math. Lett. 52 (2016), 156–161. [18] X. Yang, Y. Liu and S. Bai, A numerical solution of second-order linear partial differential equations by differential transform, Appl. Math. Comput. 173 (2006), 792–802. [19] D. Zhang and X. Miao, New unconditionally stable scheme for telegraph equation based on weighted Laguerre polynomials, Numer. Methods Partial Differ. Equ. 33 (2017), no. 5, 1603–1615. | ||
|
آمار تعداد مشاهده مقاله: 16,404 تعداد دریافت فایل اصل مقاله: 6,748 |
||