一般二阶初值问题直接解的一阶(k+3)块混合线性多步法的发展

F. Muri̇tala, M. Kolawole, A. Oyedeji, J.O. Lawal,, A.I. Alaje
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引用次数: 0

摘要

为了克服线性多步法的Dahl - Quist阶障碍,提出了块混合线性多步法。本研究旨在回答与块混合方法在求解初值问题(IVPs)时的收敛性、准确性和有效性有关的问题。本文提出了一种阶(k+3)块混合法,适用于求解常微分方程IVP的直接解。在选定的网格点上对幂级数进行搭配和插值,提高了方法的一致性、收敛性、精度和零稳定性。通过对线性问题的求解,验证了所提方法的准确性和高效性,并通过精确和近似结果的比较得到了所提方法的误差,证明了所提方法在求解该类问题时的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Development of an Order (k+3) Block-Hybrid Linear Multistep Method for the Direct Solution of General Second Order Initial Value Problems
Block hybrid linear multistep method was proposed to overcome the Dahl Quist order barrier for linear multistep methods. This research aims to answer questions relating to the convergence, accuracy, and effectiveness of the block hybrid method when utilized to obtain the solution of Initial Value Problems (IVPs). In this research, an order (k+3) block hybrid method applicable to obtain the direct solution of IVP’s of ordinary differential equations (ODEs) is presented. Collocation and interpolation of power series at finely selected grid points were used to improve the method’s consistency, convergence, accuracy and zero stability. Linear problems were solved to show the accuracy and efficiency of the proposed method, and the error obtained from the comparison of exact and approximate results shows that the proposed method is effective in solving the class of problem.
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