Convergence of the "predictor ? corrector" difference scheme for a first-order linear hyperbolic system of equations with variable coefficients

1994 ◽  
Vol 69 (5) ◽  
pp. 1267-1274
Author(s):  
A. V. Kuz'min
Keyword(s):  
Difference Scheme ◽  
Hyperbolic System ◽  
Variable Coefficients ◽  
System Of Equations ◽  
Order Linear ◽  
First Order ◽  
Hyperbolic System Of Equations ◽  
Predictor Corrector ◽  
Linear Hyperbolic System

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

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