Legendre–Galerkin spectral approximation for a nonlocal elliptic Kirchhof-type problem

ABSTRACT

We propose a numerical scheme to obtain an approximate solution of a nonlocal elliptic Kirchhof-type problem. We first reduce the problem to a nonlinear finite dimensional system by a Legendre–Galerkin spectral method and then solve it by an iterative process. Convergence of the iterative process and an error estimation of the approximate solution is provided. Numerical experiments are conducted to illustrate the performance of the proposed method.

KEYWORDS:

• Legendre–Galerkin spectral method
• iterative scheme
• nonlocal
• elliptic
• Kirchhoff problem
• error estimate

2010 AMS SUBJECT CLASSIFICATIONS:

• 65N12
• 65N15
• 65N30
• 65N35

Acknowledgments

The authors are grateful to the referees for their helpful suggestions and valuable comments, which have greatly improved the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of this author is supported in part by E-Institutes of Shanghai Municipal Education Commission [No. E03004], NSF of China [Nos. 11471217, 11671266], Ministry of Education of China [No. 211058], Specialized Research Fund for the Doctoral Program of Higher Education [No. 20113127110003] and NSF of Shanghai [No. 16ZR1424900].