Introduction: The theory and application of nonlinear two-dimensional Fredholm integral equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving nonlinear two-dimensional Fredholm integral equations. Aim:In this paper, two-dimensional triangular orthogonal functions (2D-TFs) is applied to numerical solution of nonlinear two-dimensional Fredholm integral equations. Materials and Methods:The method is based on new vector forms for representation of 2D-TFs. This approach needs no integration, so all calculations can be easily implemented. Also a theorem is proved for convergence analysis. Results:Numerical results compared to exact solutions are reported and it is shown that using 2D-TFs are a reliable tool for the solution of nonlinear two-dimensional Fredholm integral equations. Conclusion:The present method reduces the computational difficulties of the other traditional methods and all the calculations can be made simple manipulations. Several examples were tested by applying the 2D-TFs and the results have shown remarkable performance.
