Exponentially Fitted Hybrid Methods

1 Exponentially Fitted Hybrid Methods. - Kalogiratou and Simos have considered the following method  

The Local Truncation Error of the method is of the form 0(A ) (see ref. 49 for more details), i.e. is of fourth algebraie order. 

More reeently Avdelas et al. have developed the following family of methods  

The above methods for appropriate values of the free parameters a, a bi i = 0, 1, is of algebraie order four (see ref 50 for details). Avdelas et al. ° have defined the parameters of the method in order for  

Simos and Williams have considered the following method  

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R. M. Thomas and T. E. Simos, A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrodinger equation, J. Comput. Appl. Math., 1997, 87, 215-226. 

Hybrid Sixth Algebraic Order Methods. - The exponentially-fitted methods of this category are of the form... 

Remarks and Conclusion. - (I) Resonance Problem For the resonance problem the most accurate methods are the methods derived by Simos and Williams (Case IV, Case V and Case VI of the family),20 the method derived by Simos,24 the hybrid sixth algebraic order methods derived by Thomas and Simos (Case IV and Case V of the family),25 the new phase fitted method of algebraic order eight developed in this critical review in Section 2.3.1, the eighth algebraic order exponentially-fitted method derived by Simos,30 the eighth... 

In Table 8 we present the basic characteristics of the above described hybrid methods. We note that for the classification of the exponentially fitted and trigonometrically fitted methods is based on the set of functions (120). 

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