非线性中立型泛函微分方程Runge-Kutta法的稳定性和收敛性

Stability and convergence of Runge-Kutta methods for nonlinear neutral functional differential equations

本文涉及Runge-Kutta法变步长求解非线性中立型泛函微分方程(NFDEs)的稳定性和收敛性.为此,基于Volterra泛函微分方程Runge-Kutta方法的B-理论,引入了中立型泛函微分方程Runge-Kutta方法的EB(expanded B-theory)-稳定性和EB-收敛性概念.之后获得了Runge-Kutta方法变步长求解此类方程的EB-稳定性和EB-收敛性.这些结果对中立型延迟微分方程和中立型延迟积分微分方程也是新的.

This paper concerns the stability and convergence of Runge-Kutta methods for nonlinear neutral functional differential equations （NFDEs）. Based on the B-theory of Runge-Kutta methods for Volterra functional differential equations （VFDEs）, we introduce the concepts of EB-stability and EB-convergence of Runge-Kutta methods for NFDEs and obtain EB-stability and EB-convergence results on variable stepsize Runge-Kutta meth- ods for this class of equations. These results are new even for neutral delay differential equations and neutral delay integro-differential equations.