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Nonlinear Transversal Vibration Analysis of an Axially Moving Viscoelastic Yarn in Tufting Process

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Journal of Donghua University(English Edition) 2014年第1期31卷 57-61页

作者：高晓平孙以泽陈红霞 College of Light Industry and Textile Inner Mongolia University of Technology College of Mechanical Engineering Donghua University

The nonlinear transversal vibration of axially moving yarn with time-dependent tension is investigated. Yarn material is modeled as Kelvin model. A partial differential equation governing the transversal vibration is derived from the Newton's second law.Galerkin method is used to truncate the governing nonlinear differential equation,and thus the first-order ordinary differential equation is obtained. The periodic vibration equation and the natural frequency of moving yarn are received by applying homotopy perturbation method. As a result,the condition which should be avoided during the tufting process for resonance is obtained.

关键词： nonlinear vibration transversal vibration yarn homotopy perturbation method

Approximate solution of the flow over a nonlinear magneto-hydrodynamic stretching sheet

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Chinese Physics B 2012年第3期21卷 310-313页

The approximate solution of the magneto-hydrodynamic （MHD） boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.

关键词： magneto-hydrodynamic （MHD） boundary layer flow Lie symmetry method homotopy perturbation method approximate solution

用有效的解析和数值方法估算船舶在随机横浪中的横摇运动

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Journal of Marine Science and Application 2021年第1期20卷 55-66页

作者： M.Salai Mathi Selvi L.Rajendran Marwan Abukhaled Department of Mathematics AMET(Deemed to be University)ChennaiTamil NaduIndia Department of Mathematics and Statistics American University of SharjahSharjahUAE

A steady-state roll motion of ships with nonlinear damping and restoring moments for all times is modeled by a second-order nonlinear differential equation.Analytical expressions for the roll angle,velocity,acceleration,and damping and restoring moments are derived using a modified approach of homotopy perturbation method(HPM).Also,the operational matrix of derivatives of ultraspherical wavelets is used to obtain a numerical solution of the governing equation.Illustrative examples are provided to examine the applicability and accuracy of the proposed methods when compared with a highly accurate numerical scheme.

关键词： Nonlinear damping Steady-state roll motion Ultraspherical wavelets homotopy perturbation method Analytical solution

Jacobi Elliptic Numerical Solutions for the Time Fractional Variant Boussinesq Equations

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Journal of Partial Differential Equations 2014年第3期27卷 189-199页

作者： Gepreel Khaled A Math. Departement Faculty of Science Taif University Kingdom of Saudi Arabia Mathematics Department Faculty of Science Zagazig University Egypt.

The fractional derivatives in the sense of Caputo, and the homotopy perturbation method are used to construct the approximate solutions for nonlinear variant Boussinesq equations with respect to time fractional derivative. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

关键词： homotopy perturbation method fractional calculus nonlinear time fractional variant Boussinesq equations

Numerical Solution of Fractional Differential Equations

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Applied Mathematics 2020年第11期11卷 1100-1115页

作者： Adnan Daraghmeh Naji Qatanani Aya Saadeh Department of Mathematics Faculty of Science An-Najah National University Nablus Palestine

In this article, two numerical techniques, namely, the homotopy perturbation and the matrix approach methods have been proposed and implemented to obtain an approximate solution of the linear fractional differential equation. To test the effectiveness of these methods, two numerical examples with known exact solution are illustrated. Numerical experiments show that the accuracy of these methods is in a good agreement with the exact solution. However, a comparison between these methods shows that the matrix approach method provides more accurate results.

关键词： Fractional Calculus Fractional Differential Equations homotopy perturbation method Matrix Approach method

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HAM和HPM方法求解非线性方程组

HAM和HPM方法求解非线性方程组

作者：段敏中国石油大学

学位级别：硕士

随着现代科学技术的迅速发展,科学与工程计算的许多领域中所出现的非线性问题越来越多,如何求解非线性方程组,这在非线性科学中有着重要意义。本文主要研究将各种方法应用于不同的方程中,并对各种方法进行修改或得到新的方法,或与其他... 详细信息

随着现代科学技术的迅速发展,科学与工程计算的许多领域中所出现的非线性问题越来越多,如何求解非线性方程组,这在非线性科学中有着重要意义。本文主要研究将各种方法应用于不同的方程中,并对各种方法进行修改或得到新的方法,或与其他方法相结合得到更为理想的迭代公式,分析新方法的收敛性和收敛速度。在以上理论研究基础上,通过数值试验与其他方法进行数值比较。主要用到大型数值软件matlab。取得的主要成果如下: (1)在求解非线性方程组的历史中,Newton迭代法和它的变体是解非线性方程组的经典方法,至今都是基本而重要的。重点分析了由Nenad Ujevic根据求积规则推导出了新的迭代公式,考虑迭代中导数值的计算和方法的收敛速度使其应用受到限制,针对此情况,通过采用Steffensen加速法对迭代公式进行修正,推导出一类新的无导数的非线性迭代方法,并通过数值例子表明新方法的有效性。 (2)通过上述的本质修改,我们得到的迭代公式有效的减小了计算量,提高了收敛速度,但同时使得适用范围较小。考虑到二分法具有良好的区间序列渐近收敛性以及大范围收敛性质,将二分法与新方法的结合,得到了一类求解非线性方程的新算法。数值试验表明新算法与Newton法相比更为有效。 (3) HPM是一种解决非线性方程组解的新方法。首先讨论了HPM方法的重要理论知识,其次在大量国内外文献调研的基础上对HPM及其修正进行分析研究,讨论了将HPM应用于求解非线性代数方程组,得到了新了迭代公式。通过数值试验,表明该方法的有效性。

关键词：非线性方程组 homotopy perturbation method homotopy Analysis method 迭代法收敛性