Abstract

An approximate method for solving the Cauchy problem for nonlinear first-order ordinary differential equations is considered. The method is based on using the shifted Chebyshev series and a Markov quadrature formula. Some approaches are given to estimate the error of an approximate solution expressed by a partial sum of a certain order series. The error is estimated using the second approximation of the solution expressed by a partial sum of a higher order series. An algorithm for partitioning the integration interval into elementary subintervals to ensure the computation of the solution with a prescribed accuracy is constructed on the basis of the proposed approaches to error estimation.

中文翻译：

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Chebyshev级数法计算常微分方程的近似解及其误差估计

摘要

考虑了求解非线性一阶常微分方程Cauchy问题的一种近似方法。该方法基于使用移位的Chebyshev级数和Markov正交公式。给出了一些方法来估计由某个阶数序列的部分和表示的近似解的误差。使用由高阶序列的部分和表示的解的第二近似值来估计误差。在提出的误差估计方法的基础上，构建了一种将积分间隔划分为基本子间隔以确保以规定的精度计算解的算法。