Method for obtaining corrective power-series solutions to algebraic and transcendental systems (Q2725007)

The author introduces a method to approximate solutions of algebraic and transcendental systems by power series expansions in terms of parameters. The method is applied formally and relies on several assumptions which have to be taken from the application. It is designed to solve problems in physics associated with a `small' parameter. The idea is to express the unkown variable as a power series of the parameter and using this to derive a Maclaurin type series expansion for the equation to solve. Since roots are to be found, the fact that the resulting coefficients have to vanish leads to an approximation of the solution. Several examples are given to demonstrate the method. The author further notes that the method can be implemented in computer algebra systems to automatically do the analytical calculations. Similarities with the Newton-Raphson method and numerical continuation methods are briefly mentioned.