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How to solve?
Fri, 2007-05-25 02:45 - V.Gnanaraj
How to solve the equation analytically
∂2u/∂x2 + ∂2u/∂y2 - K u =0
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R. Chennamsetti, Scientist,
R. Chennamsetti, Scientist, India
You may try to solve using separation of variables technique. Here, u = X*Y where, X and Y are two exclusive functions of x and y respetively. Substitute this in the PD.
=> (1/X)*d2X/dx2+(1/Y)*d2Y/dy = K = constant.
- Ramdas Chennamsetti
thanks
V.Gnanaraj
ASSISTANT PROFESSOR
DEPARTMENT OF MATHEMATICS
THIAGARAJAR COLLEGE OF ENGINEERING
MADURAI -625015
TAMILNADU
INDIA
For more information...
Note that this is the well-known Helmholtz equation (in 2D). ... Knowing the name of the equation will probably better help you in finding the relevant resources from the literature.
On the Web, check out:
http://mathworld.wolfram.com/HelmholtzDifferentialEquation.html
http://scienceworld.wolfram.com/physics/HelmholtzEquation.html
and, on Wikipedia:
http://en.wikipedia.org/wiki/Helmholtz_Equation
Hope this helps.
R. Chennamsetti, R&DE(E),
R. Chennamsetti, R&DE(E), INDIA
Exaclty. This is the Helmholtz equation, which is obtained from wave equation after eliminating temporal terms using separation of variables technique.
u(x,y,z,t)=X(x).Y(y).Z(z).T(t).
Thanks.