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A fast numerical algorithm based on Chebyshev-wavelet technique for solving Thomas-Fermi type equation

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Abstract

A numerical method based on Chebyshev polynomials and wavelet theory to solve the generalized Thomas-Fermi boundary value problems is proposed numerically. First, we convert the generalized Thomas-Fermi boundary value problem into the equivalent integral equation. The collocation technique based on Chebyshev wavelets is applied to obtain a nonlinear system that is then dealt with the Newton-Raphson method. We also discuss the convergence and the error bound of the current process. The exactness of the present method is tested by computing the \(L_{\infty }\) and the \(L_2\)-norm errors of several numerical problems. The obtained results are compared with the precise solution and the results obtained by the other known techniques. The advantage of the Chebyshev wavelet collocation method is that it yields better accuracy for a smaller number of collocation points.

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Acknowledgements

First author of this paper is thankful to the INSPIRE Fellowship under INSPIRE Program of Department of Science and Technology, New Delhi, India for the financial support to carry out this research work.

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  1. Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, 835215, India

    Julee Shahni & Randhir Singh

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  1. Julee Shahni
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Shahni, J., Singh, R. A fast numerical algorithm based on Chebyshev-wavelet technique for solving Thomas-Fermi type equation. Engineering with Computers 38 (Suppl 4), 3409–3422 (2022). https://doi.org/10.1007/s00366-021-01476-7

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