LEM: a new method for nonlinear mechanics - Couverture souple

Toma, Ileana

Couverture souple

ISBN 10 : 1514393174 ISBN 13 : 9781514393178

Editeur : CreateSpace Independent Publishing Platform, 2015

A propos du livre

Présentation de l'éditeur :

The Linear Equivalence Method – briefly, LEM – is author’s original method. She firstly published the idea of LEM in 1978. Unlike linearization, LEM establishes a one-to-one correspondence between the solutions of an initial nonlinear problem and the analytic solutions of a certain linear PDE. This justifies the denomination of LEM: the Linear Equivalence Method. LEM provides the users with an efficient tool that enables the free application of the methods of the linear, much easier handled and better founded that those of the nonlinear. This book is addressed to all the specialists in mathematics and/or in other domains as mechanics, engineering, physics, chemistry, biology, a.s.o., who deal with models of the form of nonlinear ordinary differential equations. The understanding of the method requires only elementary notions of differential equations, analysis and algebra: LEM was applied also by students in their graduation projects. The applications of LEM cover a large area of domains and problems: from nonlinear mechanics (the nonlinear deformation of straight bars, the buckling of a straight bar, the nonlinear double pendulum, neo-Hookean or Ogden type models) to engineering (the motion of relativistic charged particles), chemistry (the Belousov-Zhabotinskij oscillatory chemical reaction), biology (the Lotka-Volterra system), Fliess series, Lie derivatives, theory of graphs, theory of numbers etc. The regretted prof. dr. rer. nat. Petre P.Teodorescu, a professor of Mechanics at the faculty of Mathematics of the University of Bucharest and a well-known author of scientific papers and treatises, applied LEM together with Ileana Toma during 35 years. Here is his testimonial to LEM (from the preface of I.Toma’s book on LEM appeared in 2008): “The method proposed by Ileana Toma is remarkable; having the privilege of applying it, I am aware that LEM represents a powerful tool, convenient for the study of nonlinear problems, the more so useful as it can be applied to a wide range of problems. The appearance of an original scientific book always represents a special event; but I consider this particular book exceptional, as, along with the purely mathematical contribution, it also contains numerous new valuable results in various domains of the natural sciences.”

Présentation de l'éditeur :

The Linear Equivalence Method – briefly, LEM – is author’s original method. Unlike what is commonly understood by linearization, LEM establishes a one-to-one correspondence between the solutions of nonlinear and linear ordinary differential equations and systems, by means of an exponential mapping - author’s idea. This justifies the denomination of LEM - the Linear Equivalence Method. LEM provides the users with an efficient and powerful tool that enables the free application of the methods of the linear, much easier handled and better founded that those of the nonlinear. This is why the applications of LEM cover a large area of domains and problems: from nonlinear mechanics (the nonlinear deformation of straight bars, the buckling of a straight bar, the nonlinear double pendulum, neo-Hookean or Ogden type models) to engineering (the motion of relativistic charged particles), chemistry (the Belousov-Zhabotinskij chemical reaction), biology (the Lotka-Volterra system), Fliess series, Lie derivatives, theory of graphs, theory of numbers (golden number) etc. This book presents LEM and its specific techniques and algorithms deduced by using the linear frame. It also emphasizes LEM’s most pertinent applications, as mentioned above. It is addressed to all the specialists - in mathematics and/or in other domains as mechanics, engineering, physics, chemistry, biology, etc. - who deal with nonlinear ordinary differential equations and who are searching for an efficient tool to get solutions, both numerically and analytically. The understanding of the method requires only elementary notions of differential equations, analysis and algebra; in this respect, it should be mentioned that LEM was also applied by students in their graduation projects.

À propos de cette édition

• Éditeur: CreateSpace Independent Publishing Platform
• Date d'édition: 2015
• ISBN 10: 1514393174
• ISBN 13: 9781514393178
• Reliure: Broché
• Numéro d'édition: 2
• Nombre de pages: 354