Document Type : Regular paper

Authors

• Hafez Yari ¹
• Mehdi Delkhosh ²

¹ Department of Computer Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.

² Department of Mathematics and Computer Science, Bardaskan Branch, Islamic Azad University, Bardaskan, Iran.

Abstract

In this paper, an applicable numerical approximation has been proposed for solving nonlinear two-dimensional integral equations (2DIEs) of the second kind on non-rectangular domains. Because directly applying the collocation methods on non-rectangular domains is difficult, in this work, at first, the integral equation is converted to an equal integral equation on a rectangular domain, then the solution is approximated by applying 2D Jacobi collocation method, the implementation of these instructions reduces the integral equation to a system of nonlinear algebraic equations, therefore, solving this system has an important role to approximate the solution. In this paper, Newton-Krylov generalized minimal residual (NK-GMRes) algorithm is used for solving the system of nonlinear algebraic equations. Furthermore, an error estimate for the presented method is investigated and several examples confirm the accuracy and efficiency of the proposed instructions.

Keywords

• Non-rectangular domains
• 2D integral equations
• Jacobi polynomials
• Collocation method
• Newton-Krylov GMRes algorithm