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 finiteelement analysis (FEA). The set of finite difference equations are linearized using Newton's Method to findan optimal solution. Throughout the paper, the Heat-Diffusion Equation is used as an example of methodimplementation.The results from using this method were checked against a simple program written in a graduate Compu-tational Physics class and a NASTRAN case. Overall, the methodology in this paper produced results thatmatched NASTRAN and the simple case well.
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