Abstract:
An efficient numerical scheme based on the Shannon wavelet basis has been presented here for obtaining highly accurate approximate solutions of Thomas–Fermi equations (TFE) in the finite domain with various initial/boundary conditions (IC/BCs). A point transformation followed by a finite Whittaker Cardinal function approximation (FWCFA) is employed here. The formula relating exponent $n$ in the desired order of accuracy $(O(10^{-n}))$ with the resolution $J$, the lower and upper limits in the sum of FWCFA have been provided. Examples of TFE with various IC/BCs have been exercised to exhibit the elegance and efficiency of the present scheme.
Key words:Thomas–Fermi equations in the finite domain, compressed or confined atoms, statistical model for charge densities, Dirichlet’s, Neumann’s, Robin’s boundary conditions, Shannon wavelets, Whittaker Cardinal function approximation.
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