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New approximate solution for time-fractional coupled KdV equations by generalised differential transform method 认领 引用 被引量：2
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作者 刘金存 侯国林 《Chinese Physics B》 SCIE EI CAS 2010年第11期41-47,共7页
In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr... In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations. 展开更多
关键词 fractional coupled KdV equations Caputo fractional derivative differential transform method approximate analytic solution
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Recursion-transform method and potential formulae of the m×n cobweb and fan networks 认领 引用 被引量：23
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作者 谭志中 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第9期82-90,共9页
In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found ... In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms. 展开更多
关键词 recursion-transform method network model potential formula exact solution
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Solving shock wave with discontinuity by enhanced differential transform method(EDTM) 认领 引用
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作者 邹丽 王振 +2 位作者 宗智 邹东阳 张朔 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第12期1569-1582,共14页
An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of... An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution. 展开更多
关键词 enhanced differential transform method （EDTM） shock wave Pad@ tech-nique Burgers equation
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The unified transform method to the high-order nonlinear Schrodinger equation with periodic initial condition 认领 引用
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作者 Leilei Liu Weiguo Zhang +1 位作者 Jian Xu Yuli Guo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2022年第8期1-10,共10页
In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,th... In this paper,we study the high-order nonlinear Schrodinger equation with periodic initial conditions via the unified transform method extended by Fokas and Lenells.For the high-order nonlinear Schrodinger equation,the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem.The related jump matrix can be explicitly expressed based on the initial data alone.Furthermore,we present the explicit solution,which corresponds to a one-gap solution. 展开更多
关键词 periodic initial condition high-order nonlinear Schrodinger equation unified transform method Riemann–Hilbert problem
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New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology 认领 引用 被引量：5
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作者 M.M.Khader Sunil Kumar S.Abbasbandy 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期135-139,共5页
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on t... We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained. 展开更多
关键词 discretized mKdV lattice equation nonlinear differential-difference equations Laplace transform,homotopy analysis transform method
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Integral Transform Method for a Porous Slider with Magnetic Field and Velocity Slip 认领 引用 被引量：1
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作者 Naeem Faraz Yasir Khan +1 位作者 Amna Anjum Anwar Hussain 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第3期1099-1118,共20页
Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for examp... Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag.There is a slip-on both the slider and the ground in the two cases,for example,a long porous slider and a circular porous slider.By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method.Solutions are obtained for different values of Reynolds numbers,velocity slip,and magnetic field.We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long and circular sliders,whereas the magnetic effect is also noticeable. 展开更多
关键词 Porous slider MHD flow Reynolds number velocity slip integral transform method.
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Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method 认领 引用 被引量：1
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作者 宋丽哪 王维国 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第8期182-188,共7页
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Ko... By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus. 展开更多
关键词 differential transform method fractional differential equation approximate solution
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Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models 认领 引用 被引量：5
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作者 K.A.Gepreel A.M.S.Mahdy +1 位作者 M.S.Mohamed A.Al-Amiri 《Computers, Materials & Continua》 SCIE EI 2019年第9期979-994,共16页
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T... In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions. 展开更多
关键词 Reduced differential transforms method nonlinear biomathematics models SI1I2R model SIR model analytic approximate solutions qualitative analysis stability and equilibrium.
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Differential transform method for solving Richards' equation 认领 引用
9
作者 Xi CHEN Ying DAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第2期169-180,共12页
An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with interm... An approximate solution to Richards＇ equation is presented, mathematically describing a sort of unsaturated single phase fluid flow in porous media. The approach is a differential transform method （DTM） with intermediate variables. Two examples are given to demonstrate the accuracy of the presented solution. 展开更多
关键词 approximate analytical solution Richavds＇ equation differential transform method （DTM） intermediate variable
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Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model 认领 引用
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作者 Henrietta Ify Ojarikre Ideh Rapheal Ebimene James Mamadu 《Journal of Applied Mathematics and Physics》 2024年第3期819-828,共10页
Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ... Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series. 展开更多
关键词 Elzaki Transform Method European Call Black-Scholes Model Fokker-Planck Equation Market Volatility
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Analysis of the characteristics of gastrointestinal motility based on Hilbert-Huang transform method 认领 引用 被引量：1
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作者 黄标 Yan Guozheng 《High Technology Letters》 EI CAS 2008年第1期30-34,共5页
Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process... Pressure activity data as an important index of gastrointestinal （GI） motility can be obtained from the wireless radiotelemetry capsule. The Hilbert-Huang transform （HHT） method, which is more effective to process non-stationary signal, is proposed to identify the characteristics of GI motility. We decompose the pressure activity data into intrinsic mode functions （IMFs）, calculate the Hi/bert marginal spectrum and attain the peristalsis characteristics of GI tract. The IMFs represent the peristalses modes of GI tract activity embedded in the pressure data. The time-varying characteristic of the method suggests that the HHT is suitable to accommodate other non-stationary biomedical data analysis. 展开更多
关键词 intrinsic mode function empirical mode decomposition （EMD） Hilbert-Huang transform （HHT） method gastrointestinal （GI） motility
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Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem 认领 引用 被引量：1
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作者 Sharaf Mohmoud Mohamed Gubara 《Applied Mathematics》 2016年第10期1049-1056,共8页
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easi... In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology. 展开更多
关键词 Reduced Differential Transform Method Goursat Problem Adomian Decomposition Method (ADM) Variational Iteration Method (VIM)
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A Comprehensive Study of Soliton Pulse Propagation Using Modified Differential Transform Methods 认领 引用
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作者 Entsar El-Shazly Ahmed Abo-Elenin Ibrahim El-Kalla 《Journal of Applied Mathematics and Physics》 2024年第12期4183-4197,共15页
In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This s... In this article, a modified version of the Differential Transform Method (DTM) is employed to examine soliton pulse propagation in a weakly non-local parabolic law medium and wave propagation in optical fibers. This semi-analytic method has the advantage of overcoming the obstacle of the hardest nonlinear terms and is used to explain the origin of the bright and dark soliton solutions through the Schrödinger equation in its non-local form and the Radhakrishnan-Kundu-Laksmannan (RKL) equation. Numerical examples demonstrate the effectiveness of this method. 展开更多
关键词 Soliton Pulse Parabolic Law Medium Differential Transform Method Bright Solution Dark Solution Schrödinger Equation Radhakrishnan-Kundu-Laksmannan
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Analyses on normal background characteristics about deformation observation data on the basis of wavelet transform method 认领 引用
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作者 李杰 刘希强 +2 位作者 李红 毛玉华 郑树田 《Acta Seismologica Sinica(English Edition)》 2005年第1期34-42,124,共9页
Wavelet transform method is applied to measure time-frequency distribution characteristics of digital deformation data and noise. Based on the characteristics of primary modulus and stochastic white noise discriminati... Wavelet transform method is applied to measure time-frequency distribution characteristics of digital deformation data and noise. Based on the characteristics of primary modulus and stochastic white noise discrimination factor of wavelet decomposition, we analyze the variation rule of normal background and noise data from Shandong digital deformation observation data. The research results indicate that: a) 1/4 daily wave, semi-diurnal tide wave, daily wave and half lunar wave and so on quasi-periodic signal exist in the detail decomposing signal of wavelet when scale are equal to 2, 3 and 4; b) The amplitude of detail decomposing signal is the biggest when scale is equal to 3; c) The detail decomposing signal contains mainly noise corresponding to scale 1 and 5, respectively; d) We may trace the abnormal precursory which is related to earthquake by analyzing non-earthquake wavelet decomposing signal whose scale is specified from digital deformation observation data. 展开更多
关键词 wavelet transform digital deformation observation data separation method between signal and noise discrimination of earthquake precursory
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Application of the Hybrid Differential Transform Method to the Nonlinear Equations 认领 引用
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作者 Inci Cilingir Sungu* Huseyin Demir 《Applied Mathematics》 2012年第3期246-250,共5页
In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform... In this paper, a hybrid method is introduced briefly to predict the behavior of the non-linear partial differential equations. The method is hybrid in the sense that different numerical methods, differential transform and finite differences, are used in different subdomains. Our aim of this approach is to combine the flexibility of differential transform and the efficiency of finite differences. An explicit hybrid method for the transient response of inhomogeneous nonlinear partial differential equations is presented;applying finite difference scheme on the fixed grid size is used to approximate the space discretisation, whereas the differential transform method is used for time operator. Comparison of the efficiency of the different approaches is a very important aspect of this study. In our test cases, the hybrid approach is faster than the corresponding highly optimized finite difference method in two dimensional computations. We compared our hybrid approach’s results with the exact and/or numerical solutions of PDE which obtained from Adomian Decomposition Method. Results show that the hybrid approach may be an important tool to reduce the execution time and memory requirements for large scale computations and get remarkable results in predicting the solutions of nonlinear initial value problems. 展开更多
关键词 Hybrid Differential Transform/Finite Difference Method Nonlinear Initial Value Problems Numerical Solution
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Some Equivalence Transform Methods for Simulating Models in Control Systems 认领 引用
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作者 Degui, Liu 《Journal of Systems Engineering and Electronics》 EI 1993年第4期32-42,共11页
In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic ... In this paper two classes of equivalence transform methods for solving ordinary differential equations are proposed. One class of method is the equivalence integral transform method for special differential algebraic problems. The advantage of this class of method is such that the amount of work calculating one integration with parameters becomes that of two interpolations, when the system of nonlinear equations is solved on the right hand side function. The other class of method is the equivalence substitution method for avoiding calculating derivative on the right hand side function. In order to avoid calculation derivatives, two equivalence substitution methods are proposed here. The application instances of some special effect of the equivalence substitution methods are given. 展开更多
关键词 Algebra Calculations Computer simulation Control systems Differential equations Integration Interpolation Mathematical models Mathematical transformations Nonlinear equations Numerical methods
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A method of genetic transformation of Xizang medical plants without tissue culture 认领 引用 被引量：1
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作者 Ting Sun Xinghao Han +4 位作者 Yuanyuan Jiang Qiulin Li Yuanjiang Xu Fangyuan Zhang Xiaozhong Lan 《Medicinal Plant Biology》 2025年第1期424-429,共6页
Mirabilis himalaica,known for its medicinal properties and limited distribution in the Qinghai-Xizang Plateau,is under conservation pressure due to high market demand.Traditional transformation methods are inefficient... Mirabilis himalaica,known for its medicinal properties and limited distribution in the Qinghai-Xizang Plateau,is under conservation pressure due to high market demand.Traditional transformation methods are inefficient for this species,prompting the development of a non-tissue culture approach.This study utilized mature leaves as explants and employed a cut-dip-budding(CDB)system to transform fluorescence and betacyanin reporter systems in M.himalaica,successfully transforming a high-altitude Xizang medicinal plant.The study found that mature leaves exhibited robust regeneration potential,making them ideal for large-scale transformation.The transformation system achieved approximately 76%positive rooting rate and a 2%positive transgenic plant rate.This method overcomes challenges associated with Agrobacterium tumefaciens-mediated transformation and lays the foundation for future genetic research and industrial applications of Xizang medicinal plants. 展开更多
关键词 mirabilis himalaicaknown Mirabilis himalaica fluorescence reporter non tissue culture betacyanin reporter transformation methods genetic transformation transform fluorescence betacyanin reporter systems
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基于Transformer的半监督偏多标签图像分类方法 认领 引用
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作者 李艳 周志龙 祝彪 《吉林大学学报（信息科学版）》 CAS 2026年第4期851-862,共12页
针对在半监督偏多标签学习(SSPML:Semi-Supervised Partial Multi-Label Learning)方法中,特征和标签空间之间以及各自内部存在复杂的相关性,且利用标签相关性构建模型时,容易受到候选标签集中噪声标签干扰的问题,基于Transformer提出... 针对在半监督偏多标签学习(SSPML:Semi-Supervised Partial Multi-Label Learning)方法中,特征和标签空间之间以及各自内部存在复杂的相关性,且利用标签相关性构建模型时,容易受到候选标签集中噪声标签干扰的问题,基于Transformer提出一种新的半监督偏多标签图像分类算法T-SSPML(Transformer Encoder-Based Semi-Supervised Partial Multi-Label Learning)。利用Transformer编码器构建主干网络,将图像和标签特征共同作为输入,并定义新的损失函数,利用多头自注意力机制学习整体性结构信息以及标签间的关联信息。同时采用标签掩码机制,提升模型学习标签关联信息的能力。通过在多个数据集上实验结果表明,T-SSPML算法相比其他对比算法在绝大多数情况下都取得了更好的分类性能。 展开更多
关键词 偏多标签学习 半监督学习 图像分类 一致性正则化 伪标签方法 Transformer编码器
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基于CNN-Transformer架构的电磁传播损耗预测算法 认领 引用
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作者 万勇 李骏杰 +1 位作者 孙伟峰 戴永寿 《现代电子技术》 北大核心 2026年第6期43-48,共6页
为了解决传统经验传播损耗模型预测精度不足的问题,提出一种基于CNN-Transformer架构的电磁传播损耗预测算法,通过构建回归模型进行精准的传播损耗预测。通过斯皮尔曼系数法提取有效特征,利用CNN提取与传播损耗预测高度相关的浅层特征,... 为了解决传统经验传播损耗模型预测精度不足的问题,提出一种基于CNN-Transformer架构的电磁传播损耗预测算法,通过构建回归模型进行精准的传播损耗预测。通过斯皮尔曼系数法提取有效特征,利用CNN提取与传播损耗预测高度相关的浅层特征,将从卫星图像中获取的传播路径上地物特征序列进行位置编码,增强对传播路径中不同地物特征顺序对传播损耗影响的理解。最后将CNN提取的浅层特征与位置编码后的地物特征输入到Transformer模型,通过多头自注意力机制捕捉特征间的全局关联性,从而有效校正传播损耗的预测结果。实验结果表明,所提出的CNN-Transformer方法显著降低了传播损耗预测的均方根误差(RMSE),达到了3.3745 dB,同时保持了0.8956的较高确定性系数(R2)。所提的电磁传播损耗预测算法为无线通信传播特性研究领域提供了参考,具有一定的应用价值。 展开更多
关键词 电磁传播 损耗预测 Transformer CNN 斯皮尔曼系数法 地物类型 位置编码
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The Multi-Step Differential Transform Method and Its Application to Determine the Solutions of Non-Linear Oscillators 认领 引用
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作者 Vedat Suat Erturk Zaid M.Odibat Shaher Momani 《Advances in Applied Mathematics and Mechanics》 SCIE 2012年第4期422-438,共17页
In this paper,a reliable algorithm based on an adaptation of the standard differential transform method is presented,which is the multi-step differential transform method(MSDTM).The solutions of non-linear oscillators... In this paper,a reliable algorithm based on an adaptation of the standard differential transform method is presented,which is the multi-step differential transform method(MSDTM).The solutions of non-linear oscillators were obtained by MSDTM.Figurative comparisons between the MSDTM and the classical fourthorder Runge-Kutta method(RK4)reveal that the proposed technique is a promising tool to solve non-linear oscillators. 展开更多
关键词 Non-linear oscillatory systems differential transform method numerical solution
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