Stability Analysis Of A Class Of Nonlinear Functional Differential Algebraic Equations And Their Runge-Kutta Methods

Functional differential algebraic equations are widely used in biology,eco-nomics,control theory and other scientific fields.Functional differential algebraic equations are not only constrained by algebraic conditions,but also affected by factors such as delay,which increases the complexity of solving analytical solu-tions.Therefore,it is of great significance to study the numerical methods for functional differential-algebraic equations.Firstly,a class of nonlinear function-al differential algebraic equations is studied,in which the right-hand function f（t,y（t）,y（·）,z（t）,z（·））satisfy one-sided Lipschitz condition for y（t）and classical Lipschitz conditions for y（·）,z（t）and z（·）,and the algebraic conditions satisfy classical Lipschitz conditions.It is shown that the analytical solution of the equa-tions has strict contraction and asymptotic stability.Secondly,a Runge-Kutta method with canonical interpolation operator is constructed,which satisfies al-gebraic stability and W（C₁,C₂）condition,and it is proved that the numerical solutions obtained by solving the initial value problems of this kind of nonlinear functional differential algebraic equations have strict contraction and asymptot-ic stability.Numerical experiments show that the numerical solutions obtained by the 2-stage Radau II A Runge-Kutta method and the 2-stage Lobatto II-I C Runge-Kutta method with the 2-degree piecewise Lagrangian interpolation polynomial for solving nonlinear functional differential algebraic equations can maintain the strict contraction and asymptotic stability of the equations.