Nonlinear differential equations piecewise continuous linear approximation in computational structural analysis

7th International Symposium Actual Problems of Computational Simulation in Civil Engineering

土木建筑工程;计算机科学

Leibov, R.L.^1

National Research Moscow State University of Civil Engineering, 26, Yaroslavskoe Highway, Moscow

129337, Russia^1

关键词: Linear approximations;    Linear differential equation;    Nonlinear differential equation;    Piecewise linear;    Piecewise linear approximations;    Piecewise-continuous;    Random search method;    System approximation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/456/1/012116/pdf
DOI  :  10.1088/1757-899X/456/1/012116

来源: IOP

【 摘 要 】

This paper presents a piecewise-continuous approach to nonlinear differential equations system approximation problem. In many cases, the nonlinear differential equations right-hand sides' linearization is extremely difficult or even impossible. Then piecewise continuous and piecewise linear approximations of nonlinear differential equations can be used. The piecewise continuous linear differential equations can improve piecewise linear differential equations by increasing the number of separate linear differential equations systems areas and thereby reducing errors on the borders of these areas. The matrices of piecewise continuous linear differential equations system for steady-state points are estimated using nonlinear model time responses, nonlinear programming and random search method. The proposed approach application results are presented.