G-stability one-leg hybrid methods for solving DAEs

This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are sometimes described by systems of differential algebraic equations (DAEs) and ordinary differe...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2019; no. 1; pp. 1 - 15
Main Authors: Agarwal, P., Ibrahim, Iman H., Yousry, Fatma M.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 12.03.2019
Springer Nature B.V
SpringerOpen
Subjects:
A(α)-stability
Advances in Fractional Differential Equations and Their Real World Applications - Part Two
Algebra
Analysis
Control stability
Control theory
DAEs
Difference and Functional Equations
Differential equations
Functional Analysis
G-stability
Hybrid methods
Mathematical analysis
Mathematics
Mathematics and Statistics
One-leg methods
Ordinary Differential Equations
Partial Differential Equations
65L05
A
65L06
Hybrid methods
DAEs
65L20
One-leg methods
G-stability
stability
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:This paper introduces the solution of differential algebraic equations using two hybrid classes and their twin one-leg with improved stability properties. Physical systems of interest in control theory are sometimes described by systems of differential algebraic equations (DAEs) and ordinary differential equations (ODEs) which are zero index DAEs. The study of the first hybrid class includes the order of convergence, A( α )-stability, stability regions, and G-stability for its one-leg twin in two cases: for step ( k = 1 ) and steps ( k = 2 ). For the second class, G-stability of its one-leg twin is studied in two cases: for steps ( k = 2 ) and steps ( k = 3 ). Test problems are introduced with different step size at different end points.
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2019-2