SOLUTION OF THE RICCATI EQUATION.
Abstract:
The method described in this report is advanced as a means of solving a wide range of differential equations arising from scientific applications in the aerospace industry. The technique applied for solving these equations utilizes the principle that certain differential and difference equations may be thought of as the limiting form assumed by their auxiliary functions as their orders of approximations approach infinity. The auxiliary functions for differential or difference equations always have associated residual terms which vanish as the order of approximations grow large. An auxiliary function is chosen whose solution is always represented as a rational fraction. When the numerator and denominator of this rational fraction are infinite series, this rational fraction is the solution of the equation of interest provided the quotient is finite and non-trivial. Author