Asymptotic stability, contractivity and dissipativity of one-leg theta-method for non-autonomous delay functional differential equations

Abstract This paper focuses on asymptotic stability, contractivity and dissipativity of non-autonomous nonlinear delay functional differential equations with bounded lag, and the corresponding dynamical properties of one-leg θ -method. Sufficient conditions for these delay functional differential equations to be dissipative, asymptotically stable and contractive are established. One-leg θ -method is constructed to solve such equations numerically. An important result on the growth of solution of a class of difference inequalities with variable coefficients is obtained. Finally, it is proved that the one-leg θ -method is asymptotically stable, contractive and dissipative if and only if θ  = 1. Numerical examples are given to confirm our theoretical results.

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