Computational approach and convergence analysis for interval-based solution of the Benjamin–Bona–Mahony equation with imprecise parameters

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Rambabu Vana, Karunakar Perumandla
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引用次数: 0

Abstract

Purpose

To provide a new semi-analytical solution for the nonlinear Benjamin–Bona–Mahony (BBM) equation in the form of a convergent series. The results obtained through HPTM for BBM are compared with those obtained using the Sine-Gordon Expansion Method (SGEM) and the exact solution. We consider the initial condition as uncertain, represented in terms of an interval then investigate the solution of the interval Benjamin–Bona–Mahony (iBBM).

Design/methodology/approach

We employ the Homotopy Perturbation Transform Method (HPTM) to derive the series solution for the BBM equation. Furthermore, the iBBM equation is solved using HPTM to the initial condition has been considered as an interval number as the coefficient of it depends on several parameters and provides lower and upper interval solutions for iBBM.

Findings

The obtained numerical results provide accurate solutions, as demonstrated in the figures. The numerical results are evaluated to the precise solutions and found to be in good agreement. Further, the initial condition has been considered as an interval number as the coefficient of it depends on several parameters. To enhance the clarity, we depict our solutions using 3D graphics and interval solution plots generated using MATLAB.

Originality/value

A new semi-analytical convergent series-type solution has been found for nonlinear BBM and interval BBM equations with the help of the semi-analytical technique HPTM.

参数不精确的本杰明-博纳-马霍尼方程基于区间求解的计算方法和收敛性分析
目的以收敛级数形式为非线性本杰明-博纳-马霍尼(BBM)方程提供一种新的半解析解。将通过 BBM 的 HPTM 方法获得的结果与使用正弦-戈登展开法 (SGEM) 和精确解法获得的结果进行比较。我们将初始条件视为不确定条件,用区间表示,然后研究区间本杰明-博纳-马霍尼(iBBM)方程的解。此外,由于 iBBM 的系数取决于多个参数,因此初始条件被视为区间数,我们采用 HPTM 方法求解了 iBBM 方程,并为 iBBM 提供了下区间和上区间解。根据精确解对数值结果进行了评估,发现两者非常吻合。此外,初始条件被视为区间数,因为其系数取决于多个参数。为了提高清晰度,我们使用 MATLAB 生成的三维图形和区间解图来描述我们的解。
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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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