Abstract This study aims to use the Taylor wavelet method to solve linear and nonlinear Lane-Emden equations. An advantage of the method is the orthonormality property of the polynomials which reduce the computational cost. Another advantage is that the nonlinear terms do not need to be approximated. The application of the method reduces the differential equations to a system of algebraic equations. Six differential equations that model different physical problems with initial and boundary conditions are solved to illustrate the efficiency and accuracy of the Taylor wavelet method. The results obtained from the method are compared with other numerical results and exact solutions and presented in terms of absolute error tables and graphics. We observe from these results that the method is highly accurate and capable of obtaining the exact solution when it is in the form of a polynomial.

中文翻译：

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线性和非线性 Lane-Emden 方程的泰勒小波解

摘要 本研究旨在利用泰勒小波方法求解线性和非线性Lane-Emden方程。该方法的一个优点是多项式的正交特性，这降低了计算成本。另一个优点是不需要近似非线性项。该方法的应用将微分方程简化为代数方程组。求解具有初始和边界条件的不同物理问题的六个微分方程，以说明泰勒小波方法的效率和准确性。将该方法获得的结果与其他数值结果和精确解进行比较，并以绝对误差表和图形的形式呈现。