Chapter 2: Numerical Methods
The basic
numerical methods involved in this WebBook (and associated Separation Processes course) are as follows:
1. Solution
of systems of linear algebraic equations using Gaussian elimination followed by
back substitution.
2. Solution
of systems of nonlinear algebraic equations using Newton's method, variations of Newton's method, direct
substitution (or fixed-point iteration) methods, and similar methods.
3.
Multivariable nonlinear optimization using Newton's method, variations of Newton's method, and similar types
of methods.
4.
Multivariable nonlinear contrained optimization using the method of Lagrange
multipliers.
5. Solution
of systems of nonlinear ordinary differential equations using Euler's method, the modified Euler's method. and
other similar methods.
All of these methods are simple to implement using either Microsoft Excel or
MATLAB, as described elsewhere in this WebBook. In particular, the 2007 (or later) version of MS Excel
includes a random multistart, generalized reduced gradient (GRG) search algorith and an evolutionary genetic
search algorith which are both reasonably effective for solving moderately nonlinear systems of nonlinear
equations and contrained optmization problems.
Additional Information:
