Series Solution of Linear Differential Equations

1963 ◽  
Vol 47 (360) ◽  
pp. 120
Author(s):  
W. G. Bickley
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Linear Differential Equations ◽  
Linear Differential

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.

scholarly journals On the asymptotic series solution of some higher order linear differential equations at turning points

1984 ◽  
Vol 7 (3) ◽  
pp. 541-548
Author(s):  
Arthur D. Gorman
Keyword(s):  
Differential Equations ◽  
Series Solution ◽  
Turning Points ◽  
Asymptotic Series ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Asymptotic Series Solution ◽  
Linear Differential

The Lagrange manifold (WKB) formalism enables the determination of the asymptotic series solution of second-order “wave type” differential equations at turning points. The formalism also applies to higher order linear differential equations, as we make explicit here illustrating with some4th order equations of physical significance.

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