一类均匀精确阶Lobatto-Runge-Kutta配置方法

IF 2.5 3区 数学 Q1 MATHEMATICS, APPLIED
D. G. Yakubu, N. Manjak, S. Buba, A. I. Maksha
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引用次数: 2

摘要

我们考虑了一个用于Lobatto-Runge-Kutta搭配方法的插值构造。主要目的是推导出单对称连续解(插值)在步进点和离步点的均匀精度,在考虑的区间内处处均匀阶数为6。我们在不同的离步点处评估连续格式,得到多混合格式,如果需要,可以同时求解密集近似。将得到的多重混合格式转换为Lobatto-Runge-Kutta配置方法,以精确求解初值问题。本文的独特之处在于将所有的离步配点集用作额外的插值点,同时通过积分恒等式在考虑的区间内的解图的各个部分下作为相等的面积自然地保持对称性。给出了实现插值的两种可能方法,并通过数值算例进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A family of uniformly accurate order Lobatto-Runge-Kutta collocation methods
We consider the construction of an interpolant for use with Lobatto-Runge-Kutta collocation methods. The main aim is to derive single symmetric continuous solution(interpolant) for uniform accuracy at the step points as well as at the off-step points whose uniform order six everywhere in the interval of consideration. We evaluate the continuous scheme at different off-step points to obtain multi-hybrid schemes which if desired can be solved simultaneously for dense approximations. The multi-hybrid schemes obtained were converted to Lobatto-Runge-Kutta collocation methods for accurate solution of initial value problems. The unique feature of the paper is the idea of using all the set of off-step collocation points as additional interpolation points while symmetry is retained naturally by integration identities as equal areas under the various segments of the solution graph over the interval of consideration. We show two possible ways of implementing the interpolant to achieve the aim and compare them on some numerical examples.
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来源期刊
Computational & Applied Mathematics
Computational & Applied Mathematics Mathematics-Computational Mathematics
CiteScore
4.50
自引率
11.50%
发文量
352
审稿时长
>12 weeks
期刊介绍: Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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