Combining differential quadrature method with simulation technique to solve non-linear differential equations

Abstract

Nowadays, most of the ordinary differential equations (ODEs) can be solved by modelica-based approaches, such as Matlab/Simulink, Dymola and LabView, which use simulation technique (ST). However, these kinds of approaches restrict the users in the enforcement of conditions at any instant of the time domain. This limitation is one of the most important drawbacks of the ST. Another method of solution, differential quadrature method (DQM), leads to very accurate results using only a few grids on the domain. On the other hand, DQM is not flexible for the solution of non-linear ODEs and it is not so easy to impose multiple conditions on the same location. For these reasons, the author aims to eliminate the mentioned disadvantages of the simulation technique (ST) and DQM using favorable characteristics of each method in the other. This work aims to show how the combining method (CM) works simply by solving some non-linear problems and how the CM gives more accurate results compared with those of other methods. Copyright © 2008 John Wiley & Sons, Ltd.