A NEW CLASS OF A(α)-STABLE k-STEP IMPLICIT METHODS OF ORDER k
一类A(α)稳定的k阶线性k步法公式

In this paper a new class of linear k-step implicit methods of order k,similar to Gear methods,is given.The fractal coefficients of the formulas of order 2 to 6 in this class are deduced,the orders and error coefficients are also gotten.Then we proved that they are A(α)- stable and the radiant angles of stabilityαare given.Finally,by means of the comparison numerical experiment,it is verified that they are stable and suitable for solving initial value problems of stiff ordinary differential equations.