An approach to using Chebyshev series to solve canonical second-order ordinary differential equations is described. This approach is based on the approximation of the solution to the Cauchy problem and its first and second derivatives by partial sums of shifted Chebyshev series. The coefficients of the series are determined by an iterative process using the Markov quadrature formula. It is shown that the described approach allows one to propose an approximate analytical method of solving the Cauchy problem. A number of canonical second-order ordinary differential equations are considered to represent their approximate analytical solutions in the form of partial sums of shifted Chebyshev series.

中文翻译：

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二阶常微分方程组近似解的一种解析方法

描述了一种使用切比雪夫级数解经典二阶常微分方程的方法。这种方法是基于柯西问题及其一阶和二阶导数的近似解，即通过偏移切比雪夫级数的和求和。该级数的系数是使用Markov正交公式通过迭代过程确定的。结果表明，所描述的方法允许人们提出一种解决柯西问题的近似分析方法。考虑使用许多规范的二阶常微分方程以偏移切比雪夫级数和的形式表示其近似解析解。