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[itex]y^*(x)=Ʃc_iN_i(x)[/itex] where i lies between 1 and n

where y* is the approximate solution expressed as the product of ci unknown,

constant parameters to be determined and Ni (x ) trial functions.

The major requirement placed on the trial functions is that they be admissible functions;

that is, the trial functions are continuous over the domain of interest and satisfy

the specified boundary conditions exactly. In addition, the trial functions should

be selected to satisfy the “physics” of the problem in a general sense.

Given these somewhat lax conditions, it is highly unlikely that the solution represented by

above equation is exact. Instead, on substitution of the assumed solution into the

main differential equation a residual error results.

The method of weighted residuals requires that the unknown parameters ci be evaluated such that:

[itex]∫w_i(x)R(x)dx = 0[/itex]

**Can anyone please explain the physical interpretation of the above equation?The physical significance of**

What are these weights physically signify?

*weights*?What are these weights physically signify?

What is the maigic in these weights such that error (residue) is 0?

Vishal