Constructing And Analysis Of Universal Difference Schemes Of Several Non-linear Evolution Equations

For seven non-linear evolution equations having great impotrtance physical background:advection equation,Burgers equation,KdV equation,mKdV equation, KdV-Burgers equation,CKdV equation and Fisher equation,this paper constructs new universal difference schemes(θschemes),analyze stability ofθschemes by heuristic analysis and obtain stability evidences of schemes and analyze the accuracy of the numerical solution;The main results in this paper include:(1)Followθschemes of non-linear advection equation and Burgers are highly effective,many schemes in the present are its special cases;(2)Analysis and New universal numerical experiment show difference sehemes (θschemes) in this paper are practical and effective;(3)Computational stability ofθschemes of non-linear evolution equations has something with the structure and initial value of schemes and its partial derivative.