Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics - Hardcover

Shalashilin, V.I.; Kuznetsov, E. B.

Hardcover

ISBN 10: 1402015429 ISBN 13: 9781402015427

Publisher: Springer, 2003

Synopsis

A decade has passed since Problems of Nonlinear Deformation, the first book by E.I. Grigoliuk: and V.I. Shalashilin was published. That work gave a systematic 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 algorithm can efficiently work for building up any parametric set. This fact significantly widens its potential applications. A curve is the simplest example of such a set, and it can be used for solving various problems, inc1uding the Cauchy problem for ordinary differential equations (ODE), interpolation and approximation of curves, etc. Research in this area has led to exciting results. The most interesting of such is the understanding and proof of the fact that the length of the arc calculated along this solution curve is the optimal continuation parameter for this solution. We will refer to the continuation solution with the optimal parameter as the best parametrization and in this book we have applied this method to variable c1asses of problems: in chapter 1 to non-linear problems with a parameter, in chapters 2 and 3 to initial value problems for ODE, in particular to stiff problems, in chapters 4 and 5 to differential-algebraic and functional differential equations.

About this title

Synopsis

The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. In this book the authors consider the best parameterization for nonlinear algebraic or transcendental equations, initial value or Cauchy problems for ordinary differential equations (ODEs), including stiff systems, differential-algebraic equations, functional-differential equations, the problems of interpolation and approximation of curves, and for nonlinear boundary-value problems for ODEs with a parameter. They also consider the best parameterization for analyzing the behavior of solutions near singular points. "Parametric Continuation and Optimal Parametrization" is one of the first books in which the best parametrization is regarded systematically for a wide class of problems. It is of interest to scientists, specialists and postgraduate students working in the field of applied and numerical mathematics and mechanics.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 1402015429
• ISBN 13: 9781402015427
• Binding: Hardcover
• Number of pages: 236