Convergence of Linear Multistep Methods and One-Leg Methods for Index-2 Differential-Algebraic Equations with a Variable Delay

2012 ◽  
Vol 4 (5) ◽  
pp. 636-646 ◽  
Author(s):  
Hongliang Liu ◽  
Aiguo Xiao
Keyword(s):  
Multistep Methods ◽  
Differential Algebraic Equations ◽  
Linear Multistep Methods ◽  
Variable Delay ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Convergence Results ◽  
Index 2

AbstractLinear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay. The corresponding convergence results are obtained and successfully confirmed by some numerical examples. The results obtained in this work extend the corresponding ones in literature.

scholarly journals Discrete Waveform Relaxation Method for Linear Fractional Delay Differential-Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hongliang Liu ◽  
Yayun Fu ◽  
Bailing Li
Keyword(s):  
Time Lag ◽  
Relaxation Method ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Convergence Results ◽  
Waveform Relaxation Method ◽  
Fractional Delay ◽  
Delay Differential

Fractional order delay differential-algebraic equations have the characteristics of time lag and memory and constraint limit. These yield some difficulties in the theoretical analysis and numerical computation. In this paper, we are devoted to solving them by the waveform relaxation method. The corresponding convergence results are obtained, and some numerical examples show the efficiency of the method.

scholarly journals Biodiesel Production by Reactive Flash: A Numerical Simulation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Alejandro Regalado-Méndez ◽  
Sigurd Skogestad ◽  
Reyna Natividad ◽  
Rubí Romero
Keyword(s):  
Numerical Simulation ◽  
Differential Algebraic Equations ◽  
Biodiesel Production ◽  
Algebraic Equations ◽  
Flow Ratio ◽  
Bubble Point ◽  
Biodiesel Quality ◽  
Index 2 ◽  
Globally Stable ◽  
System Approaches

Reactive flash (RF) in biodiesel production has been studied in order to investigate steady-state multiplicities, singularities, and effect of biodiesel quality when the RF system approaches to bubble point. The RF was modeled by an index-2 system of differential algebraic equations, the vapor split (ϕ) was computed by modified Rachford-Rice equation and modified Raoult’s law computed bubble point, and the continuation analysis was tracked on MATCONT. Results of this study show the existence of turning points, leading to a unique bubble point manifold,(xBiodiesel,T)=(0.46,478.41 K), which is a globally stable flashing operation. Also, the results of the simulation in MATLAB® of the dynamic behavior of the RF show that conversion of triglycerides reaches 97% for a residence time of 5.8 minutes and a methanol to triglyceride molar flow ratio of 5 : 1.

scholarly journals Linear differential algebraic equations with constant coefficients

1970 ◽  
Vol 4 (2) ◽  
pp. 28-35 ◽  
Author(s):  
M Sahadet Hossain ◽  
M Mostafizur Rahman
Keyword(s):  
Existence And Uniqueness ◽  
Differential Algebraic Equations ◽  
Canonical Forms ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Constant Coefficients ◽  
Dae Systems ◽  
International University ◽  
Linear Differential ◽  
Modern Mathematics

Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are introduced. The canonical forms of DAEs are discussed widely to make them more efficient and easy for practical use. Also some numerical examples are discussed to clarify the existence and uniqueness of the system's solutions. Keywords: differential-algebraic equations, index concept, canonical forms. DOI: 10.3329/diujst.v4i2.4365 Daffodil International University Journal of Science and Technology Vol.4(2) 2009 pp.28-35

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