BzzNonLinearSystem

In this special case, a criterion analogous to the one proposed in Buzzi-Ferraris and Tronconi (1993) and adopted in BzzNonLinearSystem class for a generic nonlinear system based on the decrease of a norm of the vector d from an iteration to the next one is adopted. Whereas in the general case this criterion is rarely used, in this special case where the error on the variables is known, the use of this criterion is quite spontaneous (Vol. 3, Buzzi-Ferraris and Manenti, 2014). 

The BzzNonLinearSystem class is designed to solve nonlinear systems using a quasi-Newton method as the main algorithm and by availing of all the devices... 

The BzzNonLinearSystemObject class has the same constructors as the BzzNonLinearSystem class but differs from it in using as its argument a pointer to the object created by the user rather than the name of the function that evaluates the vector f (x). 

Verify the use of multiprocessors for the objects of the BzzNonLinearSystem class in a problem with dense Jacobian 500 x 500. 

BzzNonLinearSystem test(xO,TestA) char control test (3) ... 

Additional examples of the use of BzzNonLinearSystem and BzzNonLi-nearSystemObj ect classes can be found in... 

It is possible to use either an object from the BzzNonLinearSystem class or an object from the BzzNonLinearSystemObj ect class. In the former case, the program is simpler, but some global variables are needed. In the latter case, the object-oriented potential is more efficiently exploited and no global variables or functions need be used. 

Objects from the BzzNonLinearSystem class can impose constraints such as... 

BzzNonLinearSystem test(xO,Testl7 ) test.SetConstraints(xMin,xMax) ... 

Find the three solutions to the previous system using an object from the BzzNonLinearSystem class by imposing limitations on the variables. The program is... 

We also encounter this situation when we need to solve a nonlinear system using Newton s method when the Jacobian is singular at a certain iteration. This problem is relatively easy to solve when the variables for which the underdimensioned system has to be solved are known. In Chapter 7, we saw how to solve this problem using the objects from the BzzNonLinearSystem class, predisposed for square systems. Real problems are often in this fortunate position. For instance, we often know a priori which equations are algebraic and which other are differential in the case of differential-algebraic systems (Vol. 4 - Buzzi-Ferraris and Manenti, in press). If the differential equations are explicit and first order, the variables of the differential equations are known and, consequently, the variables to be used to solve the algebraic equations are known too. 

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