Numerical Stability of the Runge-Kutta Methods for Equations u′(t) = au(t)+bu(K/N*t) in Science Computation

摘要

Differential equation has widely applied in science and engineering calculation. Runge Kutta method is a main method for solving differential equations. In this paper, the numerical properties of Runge-Kutta methods for the equation u′(t) = au(t)+bu([K/N* t]) is dealed with, where K and N is relatively prime and K < N,K,N∈ Z+. The conditions are obtained under which the numerical solutions preserve the analytical stability properties of the analytic ones and some numerical experiments are given.