scholarly journals Numerical Methods for a Class of Differential Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Lei Ren ◽  
Yuan-Ming Wang
Keyword(s):  
Numerical Methods ◽  
Constant Coefficient ◽  
Numerical Experiments ◽  
Inverse Method ◽  
Padé Approximation ◽  
Differential Algebraic Equations ◽  
Drazin Inverse ◽  
Time Varying ◽  
Algebraic Equations ◽  
Pade Approximation

This paper is devoted to the study of some efficient numerical methods for the differential algebraic equations (DAEs). At first, we propose a finite algorithm to compute the Drazin inverse of the time varying DAEs. Numerical experiments are presented by Drazin inverse and Radau IIA method, which illustrate that the precision of the Drazin inverse method is higher than the Radau IIA method. Then, Drazin inverse, Radau IIA, and Padé approximation are applied to the constant coefficient DAEs, respectively. Numerical results demonstrate that the Padé approximation is powerful for solving constant coefficient DAEs.

Numerical methods for differential algebraic equations

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 141-198 ◽  
Author(s):  
Roswitha März
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Image Position

Differential algebraic equations (DAE) are special implicit ordinary differential equations (ODE)where the partial Jacobian f′y(y, x, t) is singular for all values of its arguments.

A Geometric Derivation of the Equations of Motion for Mechanical Systems With Scleronomic Constraints

2015 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Elias Paraskevopoulos
Keyword(s):  
Numerical Methods ◽  
Lagrange Multipliers ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Main Idea ◽  
Constraint Equation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Motion Constraints ◽  
Stiffness Properties

A new set of equations of motion is presented for a class of mechanical systems subjected to equality motion constraints. Specifically, the systems examined satisfy a set of holonomic and/or nonholonomic scleronomic constraints. The main idea is to consider the equations describing the action of the constraints as an integral part of the overall process leading to the equations of motion. The constraints are incorporated one by one, in a process analogous to that used for setting up the equations of motion. This proves to be equivalent to assigning appropriate inertia, damping and stiffness properties to each constraint equation and leads to a system of second order ordinary differential equations for both the coordinates and the Lagrange multipliers associated to the motion constraints automatically. This brings considerable advantages, avoiding problems related to systems of differential-algebraic equations or penalty formulations. Apart from its theoretical value, this set of equations is well-suited for developing new robust and accurate numerical methods.

CONVERGENCE ANALYSIS OF THE PSEUDOSPECTRAL METHOD FOR LINEAR DAEs OF INDEX-2

2013 ◽  
Vol 10 (04) ◽  
pp. 1350019 ◽  
Author(s):  
F. GHANBARI ◽  
F. GHOREISHI
Keyword(s):  
Approximate Solution ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Pseudospectral Method ◽  
Posteriori Error ◽  
Differential Algebraic Equations ◽  
A Posteriori ◽  
Algebraic Equations ◽  
A Posteriori Error ◽  
Index 2

This paper is concerned with the study of pseudospectral discretizations of the differential-algebraic equations (DAEs). Pseudospectral method based on Chebyshev polynomials are used to transcribe a given DAE into a system of algebraic equations. A posteriori error bound between the desired solution to the index 2, DAEs and the pseudospectral approximate solution of the problem is estimated in the weighted L2 norm. Some numerical experiments are considered to demonstrate the efficiency and the applicability of the method.

scholarly journals Solution of nonlinear equations via Pade approximation. A Computer Algebra approach

2021 ◽  
Vol 66 (2) ◽  
pp. 321-328
Author(s):  
Radu T. Trimbitas
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Computer Algebra ◽  
Padé Approximation ◽  
High Order ◽  
Pade Approximation ◽  
Algebra Approach

"We generate automatically several high order numerical methods for the solution of nonlinear equations using Pad e approximation and Maple CAS."

Numerical Methods for Mathematical Models of Heterogeneous Catalytic Fixed Bed Chemical Reactors

2012 ◽  
Vol 11 (1) ◽  
pp. 49-64
Author(s):  
P. D. Devika ◽  
P. A. Dinesh ◽  
G. Padmavathi ◽  
Rama Krishna Prasad
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Fixed Bed ◽  
Differential Algebraic Equations ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Chemical Reactors ◽  
Catalytic Systems ◽  
Heterogeneous Catalytic ◽  
Catalytic Material

Mathematical modeling of chemical reactors is of immense interest and of enormous use in the chemical industries. The detailed modeling of heterogeneous catalytic systems is challenging because of the unknown nature of new catalytic material and also the transient behavior of such catalytic systems. The solution of mathematical models can be used to understand the interested physical systems. In addition, the solution can also be used to predict the unknown values which would have been otherwise obtained by conducting the actual experiments. Such solutions of the mathematical models involving ordinary/partial, linear/non-linear, differential/algebraic equations can be determined by using suitable analytical or numerical methods. The present work involves the development of mathematical methods and models to increase the understanding between the model parameters and also to decrease the number of laboratory experiments. In view of this, a detailed modeling of heterogeneous catalytic chemical reactor systems has been considered for the present study.

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