Applications of two-dimensional triangular functions for solving nonlinear class of mixed Volterra–Fredholm integral equations

An efficient numerical method is proposed for solving nonlinear mixed type Volterra–Fredholm integral equations, using two-dimensional orthogonal triangular functions (2D-TFs) in a direct approach. Some properties of 2D-TFs are novelty determined and an operational matrix for integration in mixed type is prepared. Since this approach does not need any integration, all calculations would be easily implemented, and it has several advantages in reducing computational burden. Finally by comparison of numerical results, accuracy and efficiency of the method will be shown.