Research On The Difference Methods For Convection-diffusion Equations

A new kind of characteristic-difference scheme is proposed for solving convecti -on diffusion equations with the linear interpolation method.The method is based on the cubic-spline difference formular of fourth-order accuracy for second order deriva -tives developed byTian Zhenfu.The stability of the characteristic difference scheme is studied.The results prove that our method is better than the ordinary characteristic difference scheme with the linear interpolation method. Based on the Saul'yev asymmetric schemes, a new alternating group explicit (AGE)method for solving convection-diffusion equation is derived in this paper. The method has the obvious property of parallelism,and is unconditionally stable. Numer -ical example is given which illustrated that the present method is in preference to Evans and Abdullah'AGE method for solving the convection-diffusion equation in [15]. A new kind of characteristic-difference scheme for convection-dominated diffus -ion equations is constructed by combining characteristic method with the finite -difference method and with the skew linear interpolation method. The convergence of the characteristic-difference scheme is studied. The advantage of this scheme is very adaptable to obtain the solution of the equations with variable coefficient and can eliminate the numerical oscillations more efficiently.