%0 Journal Article
%T A new reproducing kernel method for solving the second order partial differential equation
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Foroutan, Mohammadreza
%A Morovvati Darabad, Soheyla
%A Fallahi, Kamal
%D 2023
%\ 02/01/2023
%V 14
%N 2
%P 327-339
%! A new reproducing kernel method for solving the second order partial differential equation
%K Reproducing kernel Hilbert space method
%K shifted Chebyshev polynomials
%K Convergence analysis
%K Second order linear partial differential equation
%R 10.22075/ijnaa.2022.24802.2832
%X 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.
%U https://ijnaa.semnan.ac.ir/article_6913_f19d741b07a8bb3b33c61667f8d93be7.pdf