The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

Kunjan Shah; Twinkle Singh

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The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

机译：新的积分变换和同态摄动方法的混合解决纳米技术中的停产问题

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In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.

机译：为了解决纳米技术中出现的非线性微分-微分方程，提出了一种基于新的积分变换和同伦扰动混合的可靠算法。纳米尺度上的连续谱假说是无效的，微分-差异模型被认为是描述不连续问题的替代方法。该技术无需任何离散化或限制性假设即可找到解决方案，并避免了舍入误差。将近似解与精确解进行比较表明，该方法非常有效。它提供了更现实的级数解，可以非常迅速地收敛于非线性实际物理问题。

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《Open Journal of Applied Sciences》 |2015年第11期|共8页
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Kunjan Shah; Twinkle Singh;
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中图分类化工过程（物理过程及物理化学过程）;
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1. New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology [J] . M.M.Khader, Sunil Kumar, S.Abbasbandy 中国物理：英文版 . 2013,第011期

机译：解决纳米技术不连续性问题的新的同伦分析变换方法
2. A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method [J] . Kunjan Shah, Twinkle Singh Journal of Geoscience and Environment Protection . 2015,第4期

机译：新积分变换和同伦摄动混合法求解流体通过多孔介质的纵向扩散现象的Burger方程方程的求解
3. Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations [J] . Artion Kashuri, Akli Fundo, Matilda Kreku Advances in Pure Mathematics . 2013,第3期

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4. Adomian's decomposition method and homotopy perturbation method in solving two-dimensional Volterra-Fredholm fuzzy integral equations [C] . Atanaska Georgieva, Iva Naydenova International Conference on New Trends in the Applications of Differential Equations in Sciences . 2021

机译：Adomian的分解方法和同型扰动方法解决二维Volterra-Fredholm模糊积分方程
5. Extending and Simplifying Existing Piecewise-Linear Homotopy Methods for Solving Nonlinear Systems of Equations [D] . Wheaton, Ira, Jr. 2017

机译：求解方程组非线性系统的现有分段线性同伦方法的扩展和简化
6. Modified homotopy perturbation method for solving hypersingular integral equations of the first kind [O] . Z. K. Eshkuvatov, F. S. Zulkarnain, N. M. A. Nik Long, -1

机译：求解第一类超奇异积分方程的改进的同伦摄动方法
7. The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology [O] . Kunjan Shah, Twinkle Singh 2015

机译：新的整体变换和同型扰动方法的混合，以解决纳米技术出现的停止问题

The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

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