ABSTRACT
The term approximation methods usually refers to an analytical process that generates a symbolic approximation rather than a numerical one. The method of multiple scales is a singular method that is sometimes useful if the regular perturbation method fails. In this case the assumption is made that the solution depends on two or more different length or time scales. By trying various possibilities, one can determine those scales. The scales are treated as dependent variables when transforming the given ordinary differential equation into a partial differential equation, but then the scales are treated as independent variables when solving the equations. If it is known that the solution of a differential equation has a power series in the independent variable.
