Dissipativity Of Runge-Kutta Methods And Linear Multistep Methods For Nonlinear Neutral Delay Integro-Differential Equations

This paper is concerned with the dissiptivity of numerical methods for non-linear neutral delay integro-diferential equationsWhere Ï„1, Ï„2are positive constants and Ï„=max{Ï„1, Ï„2}, N∈Cd×dis a constantmatrix satisfing N <1, φ:[Ï„,0]â†'Cdis a continuous function, where γ, α, β, ω, c are real constants and γ≥0, β≥0, ω≥0,, denotes innerproduct and is the corresponding norm, and matrix norm belong to the vectornorm.The main results obtained in this paper are listed as follows.1) The dissipativty results of lower order Runge-Kutta methods with linearinterpolation and repeated trapezoidal rule are obtained.2) The dissipativty results of higher order Runge-Kutta methods with higherorder Lagrange interpolation and higher order quadrature formula are obtained.3) The dissipativty results of a class of linear multistep methods are obtained.Finally the numerical experiments further demonstrate the validity of thetheoretical results.