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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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 2
February 2023
Pages 327-339
  • Receive Date: 07 October 2021
  • Revise Date: 15 July 2022
  • Accept Date: 07 August 2022