非线性中立型Volterra延迟积分微分方程线性θ-方法的散逸性

Dissipativity of Linear θ-methods for Nonlinear Volterra Delay-integro-differential Equations with Neutral Type

研究了非线性中立型Volterra延迟积分微分方程及数值方法的散逸性问题。给出了关于此方程理论解散逸性的充分条件,并获得了一类求解此类问题的线性θ-方法的数值散逸性结果,此结果表明所考虑的数值方法继承了该方程的散逸性。

This paper is concerned with the dissipativity of nonlinear Volterra delay-integro-differential equations with neutral type. A sufficient condition for the dissipativity of theoretical solution of the mentioned problem above is given, and the dissipativity results are obtained for a class of linear θ-methods when they are applied to these problems. The result shows that the numerical methods inherit the dissipativity of the underlying problem.