Issue No. 08 - August (1971 vol. 20)
J.R. Rowland , IEEE
Variational equations are derived as a preliminary step in determining efficient digital integration techniques for nonlinear dynamical systems. The variational approach is applied initially to linear time-invariant systems to introduce the basic concept and then to nonlinear time-varying systems. For systems containing both linear and nonlinear parts, a combination technique which uses the exact difference equation for the linear part is developed. Higher order variational equations are also derived and compared on a simple system. Numerical approximations for solving these variational equations are discussed and illustrated for a second-order mildly nonlinear example. A significant improvement in both accuracy and execution time is realized over results obtained by the conventional fourth-order Runge?Kutta method. Finally, the new approach is discussed from the viewpoint of computational experience and special limitations for practical applications.
Computational accuracy versus speed, digital integration, hybrid simulation, nonlinear ordinary differential equations, numerical approximations, real-time digital simulation, state transition method, variational technique.
J. Rowland and W. Holmes, "A Variational Approach to Digital Integration," in IEEE Transactions on Computers, vol. 20, no. , pp. 894-900, 1971.