International Journal of Nonlinear Analysis and Applications
A new reproducing kernel method for solving the second order partial differential equation
Document Type : Research Paper
Authors
Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
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
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Volume 14, Issue 2
February 2023Pages 327-339
- Receive Date: 07 October 2021
- Revise Date: 15 July 2022
- Accept Date: 07 August 2022