The Gauss-Newton Method for Discretized PDE Models

Rather than discretizing the PDEs for the state variables and the sensitivity coefficients in order to solve them numerically at each iteration of the Gauss-Newton method, it is preferable to discretize first the governing PDEs and then 

If for example we discretize the region over which the PDE is to be solved into M grid blocks, use of finite differences (or any other discretization scheme) to approximate the spatial derivatives in Equation 10.1 yields the following system of ODEs  

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