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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

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Communications in Theoretical Physics 2012年第8期58卷 182-188页

作者：宋丽哪王维国 Center for Econometric Analysis and Forecasting School of Mathematics and Quantitative Economics Dongbei University of Finance and Economics

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.

关键词： differential transform method fractional differential equation approximate solution

The Multi-Step differential transform method and Its Application to Determine the Solutions of Non-Linear Oscillators

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Advances in Applied Mathematics and Mechanics 2012年第4期4卷 422-438页

作者： Vedat Suat Erturk Zaid M.Odibat Shaher Momani Department of Mathematics Faculty of Arts and SciencesOndokuz Mayis University55139SamsunTurkey Prince Abdullah Bin Ghazi Faculty of Science and IT Al-Balqa Applied UniversityAl-Salt 19117Jordan The University of Jordan Faculty of ScienceDepartment of MathermaticsAmman 1194Jordan

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 *** 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.

关键词： Non-linear oscillatory systems differential transform method numerical solution

Thermal analysis of a constructal T-shaped porous fin with simultaneous heat and mass transfer

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Chinese Journal of Chemical Engineering 2017年第9期25卷 1121-1136页

作者： Saheera Azmi Hazarika Tuhin Deshamukhya Dipankar Bhanja Sujit Nath Department of Mechanical Engineering National Institute of Technology

The present work establishes an analytical model for computing the temperature distribution, fin efficiency and optimum design parameters of a constructal T-shaped porous fin operating in fully wet condition. For more practical results, this study considers a cubic polynomial relationship between the humidity ratio of saturated air and the corresponding fin surface temperature. The temperature distribution has been determined by solving the highly non-linear governing equations using a semi-analytical transformation technique called differential transform method. A comparison of the results with that of a numerical model shows that this transformation method is a very efficient and convenient tool for solution of non-linear problems. The effects of various geometric, thermo-physical and psychometric parameters on the temperature distribution, fin efficiency and optimum design condition have been investigated. Also, a comparison has been presented between solid and porous fins and the results point out that by selecting an appropriate value of porosity, the heat transfer rate can be increased than the corresponding solid fin.

关键词： Constructal Porous Mass transfer Analytical Optimization differential transform method

DTM Simulation of Peristaltic Viscoelastic Biofluid Flow in Asymmetric Porous Media： A Digestive Transport Model

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Journal of Bionic Engineering 2015年第4期12卷 643-655页

作者： Dharmendra Tripathi Osman Anwar Beg Praveen Kumar Gupta Ganjam Radhakrishnamacharya Jagannath Mazumdar Department of Mechanical Engineering Manipal University Jaipur Jaipur 303007 India Gort Engovation-Bio-Propulsion Research Gabriel's Wing House Bradford BD6 1FA UK Department of Mathematics National Institute of Technology Silchar Silchar 788010 India Department of Mathematics National Institute of Technology Warangal 506004 India School of Electrical & Electronic Engineering The University of Adelaide Adelaide SA 5005 Australia

A biofluid dynamics mathematical model is developed to study peristaltic flow of non-Newtonian physiological liquid in a two-dimensional asymmetric channel containing porous media as a simulation of obstructed digestive （intestinal） transport. The fractional Oldroyd-B viscoelastic rheological model is utilized. The biophysical flow regime is constructed as a wave-like motion and porous medium is simulated with a modified Darcy-Brinkman model. This model is aimed at describing the diges- tive transport in intestinal tract containing deposits which induce impedance. A low Reynolds number approximation is em- ployed to eliminate inertial effects and the wavelength to diameter ratio is assumed to be large. The differential transform method （DTM）, a semi-computational technique is employed to obtain approximate analytical solutions to the boundary value problem. The influences of fractional （rheological material） parameters, relaxation time, retardation time, amplitude of the wave, and permeability parameter on peristaltic flow characteristics such as volumetric flow rate, pressure difference and wall friction force are computed. The present model is relevant to flow in diseased intestines.

关键词： peristaltic transport fractional Oldroyd-B model porous medium differential transform method asymmetricchannel obstructed digestive flow

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1473-1486页

作者： Aziz Khan Sana Ullah Kamal Shah Manar A.Alqudah Thabet Abdeljawad Fazal Ghani Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Mathematics Abdul Wali Khan UniversityMardanP.O.Box 23200Khyber Pakhtunkhwa23200Pakistan Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah bint Abdurahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or *** working of the fluid is described in the *** can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear *** observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using *** plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

关键词： Mass transfer micropolar flow porous channel similarity variables differential transform method

Analysis of various semi-numerical schemes for magnetohydrodynamic(MHD)squeezing fluid flow in porous medium

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Propulsion and Power Research 2019年第1期8卷 69-78页

作者： Inayat Ullah M.T.Rahim Hamid Khan Mubashir Qayyum Department of Mathematics Edwardes College PeshawarKhyber Pakhlunkhwa(KPK)25000Pakistan Department of Humanities FAST NUCES Peshawar CampusKhyber Pakhlunkhwa(KPK)25000Pakistan

In this article comparative analysis of various semi-numerical schemes has beenmade for the case of squeezing flow of an incompressible viscous fluid between two largeparallel plates having no-slip at the *** medium of flow contains magnetohy-drodynamic(MHD)effect and having small *** boundary value problem is solvedanalytically using Optimal homotopy asymptotic method(OHAM),homotopy perturbationmethod(HPM),differential transform method(DTM),Daftardar Jafari method(DIM)andAdomian decomposition method(ADM).For comparison purpose,residuals of these schemeshave been found and analyzed for *** study indicates that DTM and DJM arequite good in tem of accuracy near the center of domain[—1,1]but the accuracy reducesconsiderably near the start and end of the given *** and OHAM residuals indicatethat OHAM surpasses HPM in terms of accuracy in the present case.

关键词： Optimal homotopy asymptotic method Homotopy perturbation method differential transform method Daftardar Jafari method Adomian decomposition method Residual

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

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Frontiers of Mechanical Engineering 2014年第2期9卷 191-202页

作者： Alborz MIRZABEIGY Firooz BAKHTIARI-NEJAD Department of Mechanical Engineering Amirkabir University of Technology Hafez Ave Tehran 15914 Iran

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bemoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method （DTM） has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.

关键词： free vibration cracked beam elastic foundation restrained ends differential transform method

Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

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Propulsion and Power Research 2014年第1期3卷 41-47页

作者： Sobhan Mosayebidorcheh D.D.Ganji Masoud Farzinpoor Department of Mechanical Engineering Islamic Azad UniversityNajafabad BranchIsfahanIran Department of Mechanical Engineering Babol University of TechnologyBabolIran Department of Mechanical Engineering Islamic Azad UniversityKhomeini-Shahr BranchIsfahanIran

In this paper,differential transform method(DTM)is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer *** DTM,the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally,the coefficients of power series are obtained based on the solution of this set of *** overcame on nonlinearity without using restrictive assumptions or *** are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem *** results are compared with special case of the problem that has an exact closed-form solution,and an excellent accuracy is observed.

关键词： differential transform method Nonlinear heattransfer equation Power-law temperature dependent Temperature distribu-tion Fin efficiency

Vibration characteristics analysis of tank gun barrel with nonuniform cross-section

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Acta Mechanica Sinica 2022年第6期38卷 151-166,I0003页

作者： Xun Wang Xiaoting Rui Jinghong Wang Jianshu Zhang Genyang Wu Junjie Gu Institute of Launch Dynamics Nanjing University of Science and TechnologyNanjing 210094China

The firing accuracy of a tank gun is affected significantly by the flexural motion of the *** the purpose of satisfying the requirement of efficiently and accurately dynamic analysis and optimization of the tank gun barrel to ensure it has good dynamic characteristics and firing accuracy,the high-fidelity dynamic model of a tank gun barrel is developed according to the transfer matrix method for multibody system which has features of high degree of stylization and high computational *** transfer matrix of the non-uniform Euler-Bernoulli beam(NU-EB beam)is deduced from governing differential equations of motion utilizing the differential transform *** orthogonality of augmented eigenvectors for the NU-EB beam is proven which can be used for its exact dynamics response analysis using the modal *** allusion to the tank gun barrel with non-uniform cross-section,the barrel is modeled as a combination of several uniform and non-uniform transverse vibrating Euler-Bernoulli *** overall transfer equation and matrix of the tank gun barrel are established according to the automatic deduction theorem of the overall transfer equation of multibody *** present method is proven to be effective by comparing the computational results to those in published *** vibration characteristics of a tank gun barrel with a non-uniform cross-section are analyzed accurately and are verified by the modal test.

关键词： Tank gun barrel Transfer matrix method for multibody system differential transform method Vibration characteristics Non-uniform Euler-Bernoulli beam