Ton-Raphson

Box 5. New temperatures are calculated from the enthalpy balances Eq. (13.186). The temperature is implicit in these equations because of its involvement in the enthalpies and the Kg. Accordingly, the temperature must be found by the New-ton-Raphson method for simultaneous nonlinear equations. Box 6. The convergence criterion is... 

We will now illustrate the way that equation (2.70) could be solved as part of a stiff integration package. The solution relies partly on using the New-ton-Raphson technique for solving nonlinear simultaneous equations, the principles of which will now be explained. We may describe a system of n nonlinear. 

Discuss the methods of interval halving, successive substitution, and New-ton-Raphson for solving nonlinear algebraic equations. What are their relative advantages and disadvantages ... 

In the latter case, an interpolation by cubic natural splines between the given data was used because the derivative of the overvoltage - necessary for a New-ton-Raphson iteration process and the Wagner number -is easily obtained. 

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