Abstract:

a class of runge-kutta methods charaterized only by two parameters RK_{s^{(μ,δ)  is given  so taht all s-stage runge-kutta methods with distinct abscissas in the interval [0,1],if consisistent of order at less 2s-1 ,are recovered as special cases .for these methods both a-stability or algebraic stability are all equivalent to the condition μ≧,this criteria is an improvement of a famous result by burrage ([3],theorem 4.6.11).based on the methods of this class arbitrarily high order exponentially fitted methods are offered which are algebraically stable and therefore suitable for integration with a large stepsize for fast decaying components of stiff systems.}}

Key words: Ｔｗｏｐａｒａｍｅｔｅｒｓ, ＲｕｎｇｅＫｕｔｔａＭａｔｈｏｄｓ, Ｈｉｇｈｏｒｄｅｒ．