Convergence Analysis Of Numerical Methods For A Class Of Nonlinear Neutral Delay Differential Equations

This paper is concerned with the convergence of the numerical methods fornonlinear NDDEs:whereÏ„₁,Ï„₂ is a real positive constant,Ï„=max{Ï„₁,Ï„₂),Φ:[-Ï„,t₀]â†'C^N is acontinuous and differentiable function,the symbol(·,·)denotes inner product,thesymbol‖·‖denotes the corresponding norm,and f:[t₀,+∞]×C^N×C^N×C^Nâ†'C^Nis a continuous function satisfying whereα,(?),(?)1,(?)2 are real constants and (?)≥0,(?)1≥0,0≤(?)2<1/3we always use the symbol D(α,(?),(?)1,(?)2)to denote this problem class whichconsist of all the problems satisfying the conditions introduced aboveIn this paper,we discuss the error behaviour of this problem class,and weobtain convergence results for Runge-Kutta Methods and One-Leg Methods:1 If the method(A,b,c)is algebraically stable and diagonally stable,thenfor the problem class D(α,(?),(?)1,(?)2),it has stage order P,it is convergent of orderat least P Under certain conditions2 If an A-stable one-leg k step method(p,(9-)is consistent of order P in theclassical sense for ODEs,then for the problem class D(α,(?),(?)1,(?)2),it is convergentof order p,where s=1,2Some numerical computations show that the convergent result is correct...