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.

提出了一种基于切比雪夫多项式和小波理论的数值求解广义Thomas-Fermi边值问题的数值方法。首先，我们将广义的 Thomas-Fermi 边值问题转化为等效积分方程。应用基于切比雪夫小波的搭配技术获得非线性系统，然后用Newton-Raphson方法处理。我们还讨论了当前过程的收敛性和误差界限。通过计算\(L_{\infty }\)和\(L_2\)- 几个数值问题的范数错误。将获得的结果与精确解和通过其他已知技术获得的结果进行比较。Chebyshev 小波搭配方法的优点是它对较少数量的搭配点产生更好的准确性。