Eigen function expansion

The energy equation has been solved numerically [40] and analytically, using general Eigen functions expansion [42], and the details can be found in related references. Using the temperature distribution, the local Nusselt number may be determined as... 

Wu Z J, Ye J Q and Cabrera J G (2000) 3D analysis of stress transfer in the micromechanics of fiber reinforced composites by using an Eigen-function expansion method, J Mech Phys Solids 48 1037-1063. 

Spectral methods are used to numerically solve boundary value, eigen-value and time-dependent problems and these methods involve a completely different approach from finite-element and finite-difference methods. In spectral methods, instead of representing a function by its values at grid points, one would approximate the function by a series expansion in terms of spectral basis functions as follows (in the case of one-dimensional problem) ... 

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