publication . Article . 2017

Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

Roman Leibov;
Open Access
  • Published: 01 Jan 2017 Journal: MATEC Web of Conferences, volume 117, page 103 (eissn: 2261-236X, Copyright policy)
  • Publisher: EDP Sciences
Abstract
This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems areas. The matrices of bilinear differential equations system are estimated through nonlinear programming. The results of proposed approach application are presented.
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free text keywords: Integrating factor, Differential algebraic equation, Mathematics, Nonlinear system, Examples of differential equations, Mathematical analysis, Numerical partial differential equations, Multigrid method, Delay differential equation, Stochastic partial differential equation, lcsh:Engineering (General). Civil engineering (General), lcsh:TA1-2040
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