A new reproducing kernel method for solving the second order partial differential equation
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJNAA-14-2_026
تاریخ نمایه سازی: 26 مرداد 1402
Abstract:
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.
Keywords:
Reproducing kernel Hilbert space method , shifted Chebyshev polynomials , Convergence analysis , Second order linear partial differential equation
Authors
Mohammadreza Foroutan
Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Soheyla Morovvati Darabad
Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran
Kamal Fallahi
Department of Mathematics, Payame Noor University, P.O.Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran