On the iterative methods of linearization, decrease of order and dimension of the Karman-type PDEs

A V Krysko; J Awrejcewicz; S P Pavlov; M V Zhigalov; V A Krysko

doi:10.1155/2014/792829

On the iterative methods of linearization, decrease of order and dimension of the Karman-type PDEs

ScientificWorldJournal. 2014 Mar 16:2014:792829. doi: 10.1155/2014/792829. eCollection 2014.

Authors

A V Krysko¹, J Awrejcewicz², S P Pavlov³, M V Zhigalov³, V A Krysko³

Affiliations

¹ Engels Institute of Technology (Branch), Saratov State Technical University, Department of Higher Mathematics and Mechanics, Russian Federation, Ploschad Svobodi 17, Engels, Saratov 413100, Russia.
² Department of Automation and Biomechanics, Lodz University of Technology, and Department of Vehicles, Warsaw University of Technology, 84 Narbutta Street, 02-524 Warszawa, Poland.
³ Saratov State Technical University, Department of Mathematics and Modeling, Russian Federation, Polytehnicheskaya 77, Saratov 410054, Russia.

Abstract

Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poisson-type differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the authors.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Linear Models
Models, Theoretical*