Numerical solution of nonlinear two-dimensional Fredholm integral equations of the second kind using Sinc Nyström method

ABSTRACT

In this paper, a double-exponential (DE) Sinc Nyström method is utilized to solve nonlinear two-dimensional Fredholm integral equations of the second kind. Using the DE transformation, the Sinc quadrature rule for a definite integral is extended to double integral over a rectangular region. Therefore, a nonlinear Fredholm integral equation is reduced to a system of nonlinear algebraic equations, which is solved using the Newton iteration method. Convergence analysis shows that the proposed method can converge exponentially. Several numerical examples are provided to demonstrate the high efficiency and accuracy of the proposed method.

KEYWORDS:

• Two-dimensional
• nonlinear Fredholm integral equations
• Sinc quadrature
• Nyström method
• double-exponential transformation

2010 AMS SUBJECT CLASSIFICATION:

• 45B05
• 45G15
• 65R20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11371079).