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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
1292 LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH MAPLE
For linear second-order PDEs, we consider the classification of equations (that does not
depend on their solutions and is determined by the coefficients of the highest derivatives)
and the reduction of a given equation to appropriate canonical forms.
Let us introduce the new variables a=F
p
, b=
1
2
F
q
, c=F
r
, and calculate the discriminant
δ=b
2
ac at some point. Depending on the sign of the discriminant δ, the type of the
equation at a specific point can be parabolic (if δ=0), hyperbolic (if δ > 0), and elliptic (if
δ < 0). Let us call the equations
u
y
1
y
2
= f
1
(y
1
,y
2
,u,u
y
1
,u
y
2
), u
z
1
z
1
u
z
2
z
2
= f
2
(z
1
,z
2
,u,u
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Publisher Resources

ISBN: 9781466581494