H-stability of Runge–Kutta methods with general variable stepsize for pantograph equation

摘要

This paper deals with H-stability of Runge–Kutta methods with variable stepsize for pantograph equations. It is shown that the Runge–Kutta methods with a regular matrix A are H-stable if and only if the modulus of stability function at infinity is less than 1. Furthermore, the same conclusion can be obtained if the Runge–Kutta methods are stiffly accurate.