An algorithm for the computer simulation of very large dynamic systems

✍ Scribed by E.J. Davison

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 835 KB
• Volume: 9
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(73)90026-5

✦ Synopsis

A fast efficient algorithm may be used for integrating very large (n >> 10) stiffdifferential equations of the type R = Ax + Bu + f(x, t), x(t0) = x0, wh ere f(x, t) has a small Lipschitz constant.

Summary--An algorithm for integrating high dimensional stiff nonlinear differential equations of the type i=Ax +f(x, t)+Bu(t), x(t0)=x0, where u(t) is a specified time function, f(x, t) is a nonlinear function with a small Lipschitz constant and A is a matrix whose eigenvalues are widely distributed is given. The proposed algorithm has a truncation error of 0(hS) where h is the step-size, is numerically stable for any h provided the original system is stable and the Lipschitz constant is small enough, will give exact steady-state solutions for constant input systems for any h, and is especially suited to those systems in which the order n of the system is large, for example, n >> 10. Some numerical examples varying from 10th to 80th order are included and a comparison of the computation time required by the proposed method is made with other algorithms--the Runge--Kutta method, and Gear's method. It is found that the proposed algorithm is approximately 10 times faster than Gear's method for the 80th order example.