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首页> 外文期刊>American journal of applied sciences >Multistep Collocation Block Method for Direct Solution of Second Order Ordinary Differential Equations
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Multistep Collocation Block Method for Direct Solution of Second Order Ordinary Differential Equations

机译：直接求解二阶常微分方程的多步配点块法

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摘要

In this study, block method of order six for solving second order ordinary differential equations is developed. The method of interpolation of approximated power series and collocation of its second derivative is adopted in the derivation of the method. The developed method is applied in block form to produce approximate solution at five points simultaneously. The stability properties of the method such as order, error constants, consistency and convergence are investigated. The developed method was then applied to solve some initial value problems of second order ordinary differential equations and the numerical results indicated that the new method produced better accuracy than the existing methods when solving the same problems.
机译：在这项研究中，开发了用于解决二阶常微分方程的六阶分块方法。在该方法的推导中，采用近似幂级数的插值方法和其二阶导数的搭配方法。所开发的方法以块形式应用，以同时在五个点处产生近似解。研究了该方法的稳定性，例如阶数，误差常数，一致性和收敛性。将该方法应用于二阶常微分方程初值问题的求解，数值结果表明，该方法在求解相同问题时比现有方法具有更高的精度。

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