Parametric Continuation And Optimal Parametrization In Applied Mathematics And Mechanics
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Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics
Author: V.I. Shalashilin
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
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.
Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics
The optimal continuation parameter provides the best conditions in a linearized system of equations at any moment of the continuation process. This 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 of applied and numerical mathematics and mechanics.
Advances in Theory and Practice of Computational Mechanics
Author: Margarita N. Favorskaya
language: en
Publisher: Springer Nature
Release Date: 2022-03-30
This book is a collection of peer-reviewed best selected research papers presented at 22nd International Conference on Computational Mechanics and Modern Applied Software Systems (CMMASS 2021), held at the Alushta Health and Educational Center, The Republic of Crimea, during 4–13 September 2021. The proceedings is dedicated to solving the real-world problems of applied mechanics using smart computational technology. Physical and mathematical models, numerical methods, computational algorithms and software complexes are discussed, which allow to carry out high-precision mathematical modelling in fluid, gas and plasma mechanics, in general mechanics, deformable solid mechanics, in strength, destruction and safety of structures, etc. Smart technologies and software systems that provide effective solutions to the problems at various multi scale-levels are considered. Special attention is paid to the training of highly qualified specialists for the aviation and space industry.