Hα-stability of modified Runge–Kutta methods for nonlinear neutral pantograph equations ✩

In this paper, we investigate Hα-stability of algebraically stable Runge–Kutta methods with a variable stepsize for nonlinear neutral pantograph equations. As a result, the Radau IA, Radau IIA, Lobatto IIIC method, the odd-stage Gauss–Legendre methods and the one-leg θ-method with 12 θ 1 are Hα-stable for nonlinear neutral pantograph equations. Some experiments are given. © 2007 Elsevier Inc. All rights reserved.