Discrete Legendre spectral Galerkin method for Urysohn integral equations

ABSTRACT

In this paper, we consider the discrete Legendre spectral Galerkin method to approximate the solution of Urysohn integral equation with smooth kernel. The convergence of the approximate and iterated approximate solutions to the actual solution is discussed and the rates of convergence are obtained. In particular we have shown that, when the quadrature rule is of certain degree of precision, the superconvergence rates for the iterated Legendre spectral Galerkin method are maintained in the discrete case.

KEYWORDS:

• Urysohn integral equations
• spectral method
• discrete Galerkin method
• Legendre polynomials
• superconvergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 45B05
• 45G10
• 65R20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Guangqing Long is supported in part by the Natural Science Foundation of China under grant [11461011], Natural Science Foundation of Guangxi Education Department in China under grant [ZD2014080].