IMPLICIT FUNCTIONAL TRANSFORMATION METHOD FOR PERTURBED AND UNPERTURBED DIFFERENTIAL EQUATIONS

Implicit functional transformations in the context of ordinary differential equations are discussed. The transformations can be applied to both perturbed and unperturbed equations. The link between the general transformations and various perturbation methods is exploited. The transformations can be used basically to eliminate the secularities in the solutions, which may lead to unphysical results. For unperturbed equations, the transformations can be employed to simplify the equations, allowing for the construction of exact analytical solutions, if they exist. Numerous worked examples are provided to illustrate the applications.