Systems of multiple nonlinear algebraic equations

techniques for treating multiple nonlinear algebraic equations are required in this 

We now extend Newton s method to solve a set of N simultaneous nonlinear algebraic equations for N unknowns 

More compactly, we define the state vector of unknowns 

In a CSTR, we assume that the reactor is so perfectly mixed that the concentration field of each species is spatially uniform. That is, every point in the reactor has the same concentration of each species, governed by the set of mass balances 

V is the volumetric flow rate of the feed and outlet streams, V is the fixed reactor volume, Cj is the concentration of species j in the reactor (and in the output stream), Cj,i is the concentration of species j in the inlet stream, and k, kz are the rate constants of each chemical reaction. 

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Although MATLAB contains a built-in rontine, fsolve, for solving systems of multiple nonlinear algebraic equations (using the trnst-region Newton method discussed above), it is part of the Optimization Tooikit and so is not available in every installation of MATLAB. reduced Newton.m implements the rednced-step Newton algorithm, and can be used if... 

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