A New Method for Determining a Series Solution of Linear Differential Equations with Constant or Variable Coefficients

1926 ◽  
Vol 33 (6) ◽  
pp. 293
Author(s):  
W. O. Pennell
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
New Method ◽  
Linear Differential

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.

scholarly journals Space-time caustics

1986 ◽  
Vol 9 (3) ◽  
pp. 531-540 ◽  
Author(s):  
Arthur D. Gorman
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Series Solution ◽  
Asymptotic Series ◽  
Inhomogeneous Media ◽  
Linear Differential Equations ◽  
Spatially Inhomogeneous ◽  
Asymptotic Series Solution ◽  
Linear Differential

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of linear differential equations modelling wave propagation in spatially inhomogeneous media at caustic (turning) points. Here the formalism is adapted to determine a class of asymptotic solutions at caustic points for those equations modelling wave propagation in media with both spatial and temporal inhomogeneities. The analogous Schrodinger equation is also considered.

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