A CLASS OF LINEARLY IMPLICIT A-STABLE ONE-STEP METHODS
一类线性隐式A稳定的单步法

For Stiff initial-value problems including a system of s coupled, non-linear,first-order ordinary differential equations, a class of linearly implicit A-stable one-step methodsis developed. These methods may be derived from suitably modified A-stable one-step methodscombined with the idea of the derivation of classical Runge-Kutta methods. We have constructedk-order linearly implicit A-stable one-step methods, k = 1, 2, 3, 4. Applying such technique to Gear's method, One may obtain a class of linearly implicitstiffly stable multistep methods.