A Shannon Wavelet-Based Approximation Scheme for Thomas–Fermi Models of Confined Atoms and Ions
Sharda Kumari, Pratik Majhi, M. M. Panja · Computational Mathematics and Mathematical Physics · 2024
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.