Approximate Solutions of Algebraic Equations

Abstract

The overall theme of this and the next two chapters is the approximate analytical solution of algebraic, differential, and optimal control equations. There are several ways to get an approximate analytical solution of an equation. First, approximations can be made in the equation such that the remaining equation has an analytical solution. If the approximate solution is accurate enough, work stops. If not, something more must be done. Second, instead of discarding the small terms, they can be replaced by a small parameter, thereby creating a perturbation problem. The effect of the size of the small parameter can be investigated by simulation. Third, if the original equation contains a small parameter and if the equation with the small parameter set equal to zero has an analytical solution, a perturbation problem results.