Stability Analysis Of One-leg Methods For Functional Differential And Functional Equations

Functional differential and functional equations(FDFEs)are a class of hy—bird problem that are^rmed by functional differential equations and functionalequations The class of hybird problem arise widely in the fields of science andengineering It is meaningful to investigate the theory and application of numer—ical methods fOr FDFEs Due to the complexity of the problem．the asymptoticstability of numerical methods fOr linear FDFEs has been discussed by severalauthors Recently．YU et al investigated the stability of the problem itself andthe numerical stability of one—leg methods It is proved that any A—stable one—legmethods can preserve the stability of the problem However,the highest conver—gence order is only 2 of the A—stable one—leg methods It rflakes many coiiliilonhigher—order one—leg methods not included For these reasons,the present pa-per further study the numerical stability of G(c,P,q)一algebraically stable one—legmethodsThe main results of this paper are as^llows Firstly,we introduce the classof D(α₁,β＿1,β₂,δ,γ₁,γ₂,δ)and derive the stability condition of the problem Sec—ondly．one—leg methods are applied fOr solving the hybird problem The stabilityand asymptotic stability conditions of the G(c,P,q)一algebraically stable one—legmethods are obtained Finally,the numerical experiments are given to demon—sirate the theoretjca resl...