Abstract: This paper presents a class of high accuracy L-stable one-step method for Solving stiff ordinary differential equations on the basis of [1] and [2],which improves and extends the method introduced in [1] and [2]. In comparison with same order implicit methods,it has advantages of simple structure, less calculation,good stability and high accuracy,and it is applicable for some types of stiff problems.

Key words: Stiff ordinary differential equations, L-stable, Local truncation error, Convergence