Method for Steady State Computations

The computation of steady state solutions the equations of motion may 

the system of ODEs depends on a number of parameters but, for simplicity, we will consider the case where all but one of these is fixed. Hence, the steady state solutions will satisfy the system of algebraic equations  

In Newton s method, the quantity Ax satisfies the following system of linear algebraic equations 

If the above condition is not satisfied, X is halved until the condition holds. 

The unknowns in this system of equations are the quantities dx ldz, dxildz,. The equations can be rearranged to solve for these in terms of a particular one, dx/dz  

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