We introduce a new Iterative Finite Difference (IFD) method designed to efficiently solve highly nonlinear time-dependent problems. We propose a generalization of the IFD method, originally designed for nonlinear Ordinary Differential Equations (ODEs), to effectively address time-dependent nonlinear Partial Differential Equations (PDEs). We perform a novel high-order approximation in space and time. We perform a finite difference discretization at every iteration, leading to a generalized IFD method for solving nonlinear problems such as the known Sine-Gordon equation, Klein-Gordon equation, and the generalized Sinh-Gordon equation. Numerical simulation shows that the method has very fast convergence. It yields highly accurate solutions to the problem with a low computation cost.