ABSTRACT
Systems of simultaneous algebraic equations are frequently encountered in engineering applications such as those concerned with electrical networks, structural analysis, heat transfer, ¬uid ¬ow, optimization, vibrations, chemical reactions, and data analysis. The numerical solution of an ODE or a PDE also often reduces to the solution of a set of algebraic equations, as discussed later in Chapters 9 and 10. A system of n simultaneous equations, with x1, x2, . . ., xn as the n unknowns, may be written as
f x x x
f x x x
f x x x
( , , , )
( , , , )
( , , , )
… …
…
=
=
=
(6.1)
where f1, f2, . . ., fn denote n different functions of the n independent variables. Various methods have been developed to solve this system of equations to obtain the values of the variables x1, x2, . . ., xn. The choice of a particular method for a given problem generally depends on the nature of the equations and the number of unknowns n.
