Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran.
10.22034/cmde.2025.69615.3438
Abstract
This paper is concentrated on an investigation around a numerical scheme that gives us more precise approximations of the analytic solutions of nonlinear systems of two-dimensional integral equations in comparison with some other numerical strategies cited in the literature during recent past years. In this way, the Lagrange interpolation function together with the Legendre–Gauss quadrature formula are chosen to reach our aim. As will be observed, this method enables us to transform under study nonlinear systems of integral equations into the corresponding nonlinear algebraic systems and consequently, with the help of some standard numerical procedures such as the Newton's method for solving matrix forms of the nonlinear algebraic equations, the solutions of the obtained nonlinear algebraic systems will be obtained. The advantage of the method is that it requires relatively few collocation points to obtain a relatively small error and does not require the calculation of integrals. Thanks to these advantages, we expect to reach small and smaller error bounds for the approximated solution of the two-dimensional integral equations that is presented in frame of the convergence analysis. At the end, some illustrative numerical applications are given to justify the practical efficiency of the proposed collocation technique to numerically solve the system of two-dimensional nonlinear integral equations.
Ibrahim Neamah, F. , Sohrabi, S. and Najafi, E. (2026). On a discrete collocation method for solving nonlinear system of two-dimensional integral equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.69615.3438
MLA
Ibrahim Neamah, F. , , Sohrabi, S. , and Najafi, E. . "On a discrete collocation method for solving nonlinear system of two-dimensional integral equations", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.69615.3438
HARVARD
Ibrahim Neamah, F., Sohrabi, S., Najafi, E. (2026). 'On a discrete collocation method for solving nonlinear system of two-dimensional integral equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.69615.3438
CHICAGO
F. Ibrahim Neamah , S. Sohrabi and E. Najafi, "On a discrete collocation method for solving nonlinear system of two-dimensional integral equations," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.69615.3438
VANCOUVER
Ibrahim Neamah, F., Sohrabi, S., Najafi, E. On a discrete collocation method for solving nonlinear system of two-dimensional integral equations. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.69615.3438
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