Numerical solution of nonlinear Volterra–Fredholm integro-differential equations via direct method using triangular functions

An effective direct method to determine the numerical solution of the specific nonlinear Volterra–Fredholm integro-differential equations is proposed. The method is based on new vector forms for representation of triangular functions and its operational matrix. This approach needs no integration, so all calculations can be easily implemented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.