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In this paper,we present a new class of second derivative multistep methods and a new class of second derivative extended backward differentiation formulas.These formulas are shown to be suitable for stiff system of ordinary differential equations.The stability regions of these new methods are plotted.Numerical experiments are carried out to show strong performance of these methods.
First，we review and discuss the general linear multistep methods，linear multiderivative multistep methods and backward differentiation formulas for solving stiff problems.Then we bring out a new class of k-step(2k+1)rd order second derivative multistep methods for stiff system of differential equations and give their regions of absolute stability.At last，a new class of second derivative extended backward differentiation formulas of k-step(k+3)rd order for stiff system are proposed.The corresponding regions of absolute stability of these new methods are larger than those of Gears backward differentiation formulas，Enrights second derivative methods and Cashs extended backward differentiation formulas.
Key words：Second derivative multistep methods，region ofabsolute stability,stiffly stable，stiff system，second derivative extended backward differentiation formulas，backward differentiation formulas.