Functionals with values in the non‐Archimedean field of Laurent series and their applications to the equations of elasticity theory. II
Abstract
Functionals with values in Non‐Archimedean field of Laurent series applied to the definition of generalized solution (in the form of shock wave) of the Hopf equation and equations of elasticity theory. Calculation method for the profile of shock wave is proposed. It is shown that there is a possibility to find out some of the solutions of this system using the Newton iteration method. Examples and numerical tests are considered.
Funkcionalai su reikšmėmis ne-Archmediniuose Laurent'o sekų laukuose ir jų taikymai
elastiškumo teorijos lygtimis
Sanrtauka. Funkcionalai su reikšmėmis ne‐archimediniuose Laurent ‘o sekų laukuose pritaikyti apibrėžti apibendrintąjį Hop‘o lygties sprendinį solitono pavidalu. Pasiūlytas skaitinis algoritmas begalo siauro solitono profilio radimui. Taikant šį metodą, profilio radimas suvedamas į netiesinės algebrinių lygčių sistemos erdvėje R n+1, n > 1, sprendimą. Parodyta, kad kai kuriuos sprendinius galima surasti naudojant Niutono iteracinį metodą. Pateikiami pavyzdžiai ir skaitiniai testai.
First Published Online: 14 Oct 2010
Keywords:
generalized functions, distributions, conservation law, Hopf equation, equations of elasticity theory, soliton, shock waveHow to Cite
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2003 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.