Multiderivative Methods

Other methods, which have not yet been used in chemical kinetics, include global or passive extrapolation (see Sect. 4.5.7), averaging methods, multistep, multiderivatives methods, exponential fitting and non-linear methods (see, for example, ref. 176 for references). 

T. E. Simos, Exponentially-fitted multiderivative methods for the numerical solution of the SchrSdinger equation, J. Math. Chem., 2004, 36(1), 13-27. 

In 29 the authors have developed a trigonometrically-fitted multiderivative method for the numerical solution of the radial Schrodinger equation. The methods are called multiderivative since uses derivatives of order two and four. The method has the general form ... 

The methods are called multiderivative since uses derivatives of order two, four or six. The parameters of the method are computed in order to have eighth algebraic order and minimal phase-lag. Finally, a family of eighth algebraic order multiderivative methods with phase-lag of order 12(2)18 is developed. Numerical application of the new obtained methods to the Schrodinger equation shows their efficiency compared with other similar well known methods of the literature. 

A discussion and comparison of several multiderivative methods for molecular applications may be found in [239]. 

In [16], [34]-[35] some modified multiderivative methods are obtained. The modification is based on exponential and trigonometric fitting. 

T. E. Simos, Multiderivative Methods for the Numerical Solution of the Schrodinger Equation, MATCH Commun. Math. Comput. Chem., 2004, 45, 7-26. 

D. P. Sakas and T. E. Simos, Multiderivative methods of eighth algrebraic order with minimal phase-lag for the numerical solution of the radial Schrodinger equation. Journal of Computational and Applied Mathematics, 2005, 175(1), 161-172. 

In ref 147 the author discusses the numerical solution of second order initial value problems using multiderivative methods and especially Obrechkoff methods. More specifically the author consider the following method ... 

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