Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism

Abstract

The slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (DAEs), and therefore difficult to integrate numerically. In this work, we present the application of the differential transform method (DTM) to obtain an approximate analytical solution of the SCM model in convergent series form. In addition, we propose a posttreatment of the power series solution with the Padé resummation method to extend the domain of convergence of the approximate series solution. The main advantage of the proposed technique is that it does not require an index reduction and does not generate secular terms or depend on a perturbation parameter.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations

“…However, it is still pending for future work in order to treat DDEs with unknown exact solutions. For such hard to solve problems, we will measure the error of approximation using the mean square residual (MSR) error as in Benhammouda and Vazquez-Leal ( 2015 ). Finally, further research is required to extend this proposed methodology to other delay functions and systems of DDEs, delay differential-algebraic equations and delay partial differential equations with variable time delays.…”

“… 2007 ; Benhammouda et al. 2014b ; Benhammouda and Vazquez-Leal 2015 ; Biazar and Eslami 2010 ; Chen and Liu 1998 ; Ayaz 2004 ; Kangalgil and Ayaz 2009 ; Kanth and Aruna 2009 ; Arikoglu and Ozkol 2007 ; Chang and Chang 2008 ; Kanth and Aruna 2008 ; Lal and Ahlawat 2015 ; Odibat et al. 2010 ; El-Zahar 2013 ; Gökdoğan et al.…”

Implementation of Kalman Filtering for Differential-Algebraic Equations

“…• developing a filter which is compatible with higher order DAE's, higher order DAE's appear in constrained multi-body systems [9,60] and vehicle dynamics [61].…”

Approximate Solution of a Reduced-Type Index-kHessenberg Differential-Algebraic Control System

“…The differential-algebraic equation system is often used to model many real-life application problems arising in electrical networks, optimal control systems, and constrained multibody mechanical systems [1][2][3][4][5]. The index property is often used to characterize a differential-algebraic system, and it has been given several definitions [3,4,6].…”