Biorthogonal flatlet multiwavelet collocation method for solving the singular nonlinear system with initial and boundary conditions

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Maryam Mohseni, Davood Rostamy
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引用次数: 0

Abstract

Purpose The numerical methods are of great importance for approximating the solutions of a system of nonlinear singular ordinary differential equations. In this paper, the authors present the biorthogonal flatlet multiwavelet collocation method (BFMCM) as a numerical scheme for a class of system of Lane–Emden equations with initial or boundary or four-point boundary conditions. Design/methodology/approach The approach is involved in combining the biorthogonal flatlet multiwavelet (BFM) with the collocation method. The authors investigate the properties and procedure of the BFMCM for first time on this class of equations. By using the BFM and the collocation points, the method is constructed and it transforms the nonlinear differential equations problem into a system of nonlinear algebraic equations. The unknown coefficients of the assuming solution are determined by solving the obtained system. Additionally, convergence analysis and numerical stability of the suggested method are provided. Findings According to the attained results, the proposed BFMCM has more accurate results in comparison with results of other methods. The maximum absolute errors are calculated by using the BFMCM for comparison purposes provided. Originality/value The key desirable properties of BFMCM are its efficiency, simple applicability and minimizes errors. Therefore, the proposed method can be used to solve nonlinear problems or problems with singular points.
求解具有初始条件和边界条件的奇异非线性系统的双正交平板多小波配点法
目的数值方法对于求解非线性奇异常微分方程组具有重要意义。本文给出了一类具有初始或边界或四点边界条件的Lane-Emden方程组的双正交平板多小波配置法(BFMCM)。设计/方法/方法该方法是将双正交小波(BFM)与配位法相结合。作者首次研究了这类方程的BFMCM的性质和过程。利用BFM和配点法构造该方法,将非线性微分方程问题转化为非线性代数方程组。假设解的未知系数通过求解得到的系统来确定。此外,给出了该方法的收敛性分析和数值稳定性。结果与其他方法的结果相比,所提出的BFMCM具有更准确的结果。最大绝对误差是通过使用BFMCM来计算的,以供比较。原创性/价值BFMCM最令人满意的特性是它的效率、简单适用性和最小化误差。因此,该方法可用于求解非线性问题或具有奇异点的问题。
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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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