Baker method example problems

The complete results of the procedure, as a function of distance, are shown in Figure 3.11. For this example problem the TNO multi-energy and the Baker-Strehlow methods produce similar results. Based on the uncertainty inherent in these models, the results are essentially identical. 

Solution The system of two equations (Eqs. (4.214) and (4.215)) and two unknowns (that is and P ) for the Baker and Luks formulation can be solved via the secant method. This is just a Newton-Raphson method on numerical derivatives. Computation of the residual in Eq. (4.214) is fairly straight forward, because it only requires expressions for the second derivatives of the Helmholtz free energy/I in terms of V and These derivatives arc provided in Example 4.8. Equation (4.215) is somewhat more complicated its determinant requires derivatives of Eq. (4.214) with respect to V and N. The procedure presented in Problem 4.14 can be used to evaluate the determinant derivatives. After both residuals are computed, the system of two equations and two unknowns are solved by the Newton-Raphson method to convergence. 

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