Abstract: In this paper, a class of polynomial collocation methods with the second deriva live is derived for efficient integration of stiff systems. The methods are of one-step type, and the numerical solutions at m-point can simultaneously be obtained for each application of the formulas. It is shown that this class of methods is of order 2m+1 and the stability is analysed.

Key words: stiff ordinary differential equations, polynomial collocation methods, order, stability