Titlebook: Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics; V. I. Shalashilin,E. B. Kuznetsov Book 2003 Spri

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The Cauchy Problem for Ordinary Differential Equations,ter. This allows us to consider the Cauchy problem within the framework of the method of parametric continuation. Such a view leads to the formulation of the best continuation parameter problem, which is solved below.

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V. I. Shalashilin,E. B. Kuznetsovahrhunderte später, widmete sich in den . intensiv den aufklärerischen Möglichkeiten der Künste. Als deren wichtigste Aufgabe sah er wohl, den der Sprache Beraubten eine Stimme zu geben. Bis heute wird sich in unserer Tradition auf die antike Mythologie – sie aktualisierend und interpretierend – bezogen.

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Continuation of the Solution near Singular Points,lyzing it, to find all brunches of the solution. The complexity of the analysis depends on the degree of singularity of matrix .. We shall consider the case of simple singularity of matrix . (.(.) = . − 1), which is the most important case for applications, and also a more complicated case of its double singularity (.(.) = . − 2).

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Book 2003stematic account of the parametric continuation method. Ever since, the understanding of this method has sufficiently broadened. Previously this method was considered as a way to construct solution sets of nonlinear problems with a parameter. Now it is c1ear that one parametric continuation algorith

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Nonlinear Algebraic or Transcendental Equations with a Parameter,s parameter. A continuous smooth curve in a multidimensional space is the simplest example of such a set. For instance, it can be a solution of a system of nonlinear equations with parameter. Other examples are integral curve of Cauchy problem for a system of ordinary differential equations (ODE), interpolating or approximating curve, etc.