求解非线性二阶bvp的改进参数迭代法

IF 2.5 3区数学 Q1 MATHEMATICS, APPLIED

Computational & Applied Mathematics Pub Date : 2011-12-12 DOI:10.1590/S1807-03022011000300002

A. Ghorbani, M. Gachpazan, Jafar Saberi-Nadjafi

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引用次数: 5

摘要

原始的参数迭代法(PIM)将非线性二阶边值问题(BVP)的解作为一个迭代序列提供。由于PIM的连续迭代可能非常复杂，因此其迭代关系中的结果积分可能无法解析执行。此外，PIM的实现通常会导致不需要的项的计算，这在级数解的重复计算中消耗了更多的时间。为了克服这些困难，本文对PIM进行了有益的改进。通过对若干非线性二阶bvp的求解，证明了改进方法的实现。结果表明，该方法是求解非线性二阶微分方程的一种很有前途的分析工具，更有希望应用于求解高阶非线性微分方程，且求解精度高。数学学科分类:初级:34B15;二级:41 a10。

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A modified parametric iteration method for solving nonlinear second order BVPs

The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.

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来源期刊

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.