Solution Numerical of Stiff ODEs and DAEs in Mechanical and Other Systems

1997 ◽  
Author(s):  
H. Pasic
Keyword(s):  
Formal Solution ◽  
Differential Algebraic Equations ◽  
Single Step ◽  
Algebraic Equations ◽  
Stiff Differential Equations ◽  
Index Zero ◽  
Initial Value ◽  
Polynomial Coefficients ◽  
Multi Stage ◽  
Index 2

Abstract Presented is a formal solution of the initial-value problem of the system of general implicit differential-algebraic equations (DAEs) F(x, y, y’) = 0 of index zero or higher, based on perturbations of the polynomial coefficients of the vector y(x). The equation is linearized with respect to the coefficients and brought into a form suitable for implementation of the weighted residual methods. The solution is advanced by a single-step multi-stage collocation qadrature formula which is stiffly accurate and suitable for solving stiff differential equations and DAEs that arise in many mechanical and other systems. The algorithm is illustrated by two index-2 and index-3 examples — one of which is the well known pendulum problem.

scholarly journals A note on differential-algebraic systems with impulsive and hysteresis phenomena

2020 ◽  
pp. 51-56
Author(s):  
Pavel Petrenko ◽  
Olga Samsonyuk ◽  
Maxim Staritsyn
Keyword(s):  
Borel Measure ◽  
Impulsive Control ◽  
Generalized Solution ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Initial Value ◽  
Index 2 ◽  
Necessary And Sufficient ◽  
Uniqueness Of A Solution ◽  
Hysteresis Phenomena

n this note, we single out some promising classes of differential-algebraic equations (DAEs) with hysteresis phenomena, and propose their meaningful generalizations. We consider D Es of index 2 having two features: i) non-linearity of hysteresis type modeled by a sweeping process, and ii) impulsive control represented by a bounded signed Borel measure. For such a DAE we design an equivalent structural form, based on the Kronecker-Weierstrass transformation, and prove a necessary and sufficient condition for the existence and uniqueness of a solution to an initial value problem. We propose a notion of generalized solution to a DAE as a realization of impulsive trajectory relaxation. This relaxation is described by a dynamical system with states of bounded variation and can be equivalently represented as a system of “ordinary” DAEs.

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.

On initial value problems for ordinary differential-algebraic equations

1998 ◽  
Vol 32 (2) ◽  
pp. 61
Author(s):  
F. Leon Pritchard ◽  
William Y. Sit
Keyword(s):  
Initial Value Problems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Initial Value

scholarly journals On Asymptotics in Case of Linear Index-2 Differential-Algebraic Equations

1998 ◽  
Vol 35 (4) ◽  
pp. 1326-1346 ◽  
Author(s):  
Michael Hanke ◽  
Ebroul Izquierdo Macana ◽  
Roswitha März
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Index ◽  
Index 2

Index-2 Differential-Algebraic Equations

1989 ◽  
Vol 15 (1-2) ◽  
pp. 149-171 ◽  
Author(s):  
Roswitha März
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Index 2
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