Analytical solutions for a class of nonlinear differential equations using altran

Abstract

What follows is a discussion on the application of a digital computer to solve analytically a class of nonlinear ordinary differential equations. The asymptotic method of Krylov, Bogoliubov and Mitropolsky is employed to obtain analytical solutions. In addition, a procedure has been developed through which the initial amplitude and phase can be expressed as functions of initial displacement and velocity without the need of integration. Since the algorithms are analytical in nature, the truncated power series capability of the symbolic algebraic system ALTRAN has been used to generate analytical solutions automatically.