New Trigonometrically Fitted Dissipative Two-step Method. Case II

4 New Trigonometrically Fitted Dissipative Two-step Method. Case II. -Consider the dissipative two-step method (104). 

In order for the above method to be exact for any linear combination of the functions  

The solution of the above system of equations gives the coefficients of the method. For small values of w the formulae obtained by the solution of the system of equations are subject to heavy cancellations. In this case Taylor series expansions must be used. The local truncation error is given by  

In Appendix B we present a Maple programme for the construction of the above exponentially fitted and trigonometrically fitted dissipative two-step methods (Cases I and II). 

In Table 6 we present the basic characteristics for the dissipative methods with 

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