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.
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.
Exaclty. This is the Helmholtz equation, which is obtained from wave equation after eliminating temporal terms using separation of variables technique.
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
In reply to R. Chennamsetti, Scientist, by 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.
In reply to For more information... by Ajit R. Jadhav
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.