TWO CLASSES OF LINEARLY IMPLICIT METHODS
两类线性隐式方法

In this paper, starting with the multistep method with variable coefficients, weconstruct a class of linearly implicit multistep methods which is associated with thebackward differentiation formula (Gear's method) and a class of its corresponding "one-leg" methods. They both have accuracy order p=k for k step methods. For linearautonomous system Y=AY, these two classes of methods are identical with Gear's me-thod, moreover the first k terms of the local truncation error in the "one-leg" methodsand Gear's method are the same. Finally, the results of the numerical tests are pre-sented.