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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 | ||
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