ABSTRACT
This chapter discusses nonlinear systems, both scalar and vectoral, which arise in the modeling of physical processes as computational fluid dynamics. It illustrates the techniques, both scalar and matrix, that can be used to solve a single nonlinear equation or a set of nonlinear equations. Nonlinear matrix equations require iteration procedures for obtaining the solution vector. The Newton-Raphson technique may also be applied to nonlinear matrix systems of equations. In actual physical applications in which nonlinear matrix systems occur, a reasonable estimate for the starting iteration vector is usually the solution to the corresponding linear problem. The corresponding linear problem consists of the physical geometry, the boundary conditions, and the initial conditions of the original problem solved by a system of equations in which the nonlinear terms have been removed. Nonlinear equations have multiple roots that exist on different branches of a solution curve.
