显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性

NONLINEAR STABILITY OF EXPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

本文致力于研究巴拿赫空间中非线性中立型泛函微分方程显式和对角隐式Rung-Kutta方法的稳定性.获得了一些显式和对角隐式Rung-Kutta方法求解非线性中立型泛函微分方程的数值稳定性和条件收缩性结果,数值试验验证了这些结果.

This paper is concerned with the stability of explicit and diagonally implicit Runge- Kutta methods for nonlinear neutral functional differential equations （NFDEs） in Banach spaces. The results on the numerical stability and conditional contractivity of some explicit and diagonally implicit Runge-Kutta methods for nonlinear NFDEs are obtained. Numerical examples are given to confirm the theoretical results.