Introduction: The theory and application of nonlinearVolterra-Fredholm integro-differential equations is an important subject within physics and applied mathematics. There are several numerical approaches for solving nonlinear Volterra-Fredholm integro-differential equations. Aim: In this paper, collocation and rationalized Haar functions (RHFs) method is applied to numerical solution of nonlinear Volterra-Fredholm integro-differential equations. Materials and Methods: The properties of RHFs are first presented. These properties together with the Newton-Cotes nodes and Newton-Cotes integration method are then utilized to reduce the solution of Volterra-Fredholm integro-differential equations to the solution of algebraic equations system. Results: Its accuracy and applicability were checked on some examples. The numerical results show that the accuracy of the solutions obtained is good. Furthermore, the current method can be run with increasing s1,s2 snd k until results settle down to an appropriate accuracy. Conclusion:Finally, the method can be easily extended and applied to nonlinear VolterraFredholm integro-differential equations of arbitrary order and systems of nonlinear VolterraFredholm integro-differential equations with suitable initial coditions.
