? advantages and disvantages of numerical methods for pde

Hi:

Is it true that given a set of PDEs, one needs to solve

a set of coupled linear system of equations wether one

discretize those PDEs using FD, FE or BE method?

Are there any numerical methods that allow the user

to solve the solution of the PDEs at each single point

one at a time?

Next, one can see many literatures wrote that BEM is

more efficient than FEM for one to solve a set of PDEs.

But is that generally true or only when one can explicitly

determine the Green's function of the PDEs? For example,

only for problems that have constant parameters throughout

the whole domain. Also, BEM is more efficient only if those

target PDEs do not have volumetric source term(s)? Since

otherwise one still need to discretize the whole domain,

instead of discretizing boundary, which has one dimension

less? Any other limitations and associated reasons?

Thank you,
by Cheng Cosine
Mar/23/2k8 NC


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