Abstract

AVAZZADEH, Zakieh  and  HEYDARI, Mohammad. Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind. Comput. Appl. Math. [online]. 2012, vol.31, n.1, pp. 127-142. ISSN 1807-0302.  http://dx.doi.org/10.1590/S1807-03022012000100007.

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numerical examples. Mathematical subject classification: 65R20, 41A50, 41A55, 65M70.

Keywords : Chebyshev polynomials; two dimensional integral equations; collocation method.