Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type

作者：Song Minghui^*; Liu Mingzhu

来源：Journal of Inequalities and Applications, 2012, 290.

DOI：10.1186/1029-242X-2012-290

• stability
• oscillation
• delay differential equation
• piecewise continuous arguments

This paper is concerned with the numerical properties of Runge-Kutta methods for the alternately of retarded and advanced equation (x) over dot(t) = ax(t) + a(0)x(2[t+1/2]). The stability region of Runge-Kutta methods is determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained. A necessary and sufficient condition for the oscillation of the numerical solution is given. And it is proved that the Runge-Kutta methods preserve the oscillations of the analytic solutions. Some numerical experiments are illustrated.

• 出版日期2012
• 单位哈尔滨工业大学