Nonlinear Algebraic or Transcendental Equations with a Parameter

V. I. Shalashilin and E. B. Kuznetsov
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V. I. Shalashilin: Moscow Aviation Institute
E. B. Kuznetsov: Moscow Aviation Institute

Chapter Chapter 1 in Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics, 2003, pp 1-42 from Springer

Abstract: Abstract Solutions of many typical mathematical problems are often given by sets depending continuously on one parameter and differentiable with respect to this 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.

Keywords: Nonlinear Equation; Ordinary Differential Equation; Continuation Method; Raphson Method; Continuation Parameter (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-94-017-2537-8_1

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