The Comparison Method
The role of the comparison method, as already studied in Section II.3, might be roughly characterized as follows: the solutions of the comparison equation push on before themselves those of the original equation. Following V. M. Matrosov , this can be viewed as an interesting extension of the notion of a mathematical model. In the usual sense, a mathematical model operates approximately like the system it represents, whereas the solutions of the comparison equation fit approximately those of the original one, but while remaining “on the same side” at any time. One might speak of a one-sided model. The comparison method is sufficiently important in itself to justify the presence here of a complete chapter devoted to this subject. Further, it introduces to some typical applications.
KeywordsComparison Method Minimum Solution Differential Inequality Maximum Solution Bibliographical Note
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