A Computer-Simulated Method of Phase-Plane Displacements

Abstract

A well-known graphical phase-plane technique for solving a wide variety of ordinary second-order differential equations is shown to satisfy a relatively simple set of iterative relationships which are easily programmed on a digital computer. The only restriction on the differential equation of interest is that it can be written as aẍ + G(x, ẋ, t) = 0, where G(x, ẋ, t) = g(x, ẋ, t) + kx. Consequently, many linear and nonlinear differential equations, with or without forcing functions, which may also have (explicit) time-variable coefficients, are easily solved with the method.