This paper explores a technique to solve nonlinear partial differential equations (PDEs) using finite differences. This method is intended for higher fidelity analysis than first-order equations and quicker analysis than finite element analysis (FEA). The set of finite difference equations are linearized using Newton's Method to find an optimal solution. Throughout the paper, the Heat-Diffusion Equation is used as an example of method implementation. The results from using this method were checked against a simple program written in a graduate Computational Physics class and a NASTRAN case. Overall, the methodology in this paper produced results that matched NASTRAN and the simple case well.