Consistent extended initial value problems

To overcome this problem it has been proposed in [BES87] to solve in each subinterval [Tj Tj i] the m — 1 consistent extended initial value problems... 

It is well known that the eDF can be used for computing molecular expectation values. However, from the point of view of the development of practical applications, first order DF beginning with ab initio functions and ending as well into Atomic Shell Approximation (ASA) forms [39], are accepted work candidates for QSM applications too [40]. General QSM definition proves to contain expectation values as a particular case [41], some summarised details can be found in Appendix A. First-order eDF are customarily used in QSM molecular comparisons, since the initial description of the original concept [16]. Higher order eDF can be employed as well in QSM calculations [31,33,35]. Problems consisting in systems other than molecules can be studied in the same way [41], and the QSM applications can be extended to the area of statistical mechanics distributions [43] as well. 

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