In this paper, we used the three-dimensional triangular functions (3D-TFs) for the numerical solution of three-dimensional nonlinear mixed Volterra–Fredholm integral equations. First, 3D-TFs and their properties are described. Then the properties of 3D-TFs together with their operational matrix are used to reduce the problem to a nonlinear system of algebraic equations. Furthermore, existence and uniqueness of the solution of three-dimensional nonlinear mixed Volterra– Fredholm integral equations are proved. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique. Also, some interesting comparisons between proposed method, block-pulse functions (BPFs) method and modified block-pulse functions (MBPFs) method are presented.
