Differential transform method applied to high index differential–algebraic equations

Hong, Liu; Song, Yisheng

doi:10.1016/j.amc.2006.05.173

Cited by 75 publications

(52 citation statements)

References 10 publications

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“…Some of the fundamental theorems on differential transform can be found in [16][17][18][19][20][21].…”

Section: Differential Transform Methodsmentioning

confidence: 99%

Different Implementation Approaches of the Strong Form Meshless Implementation of Taylor Series Method

Karamanlı¹

2015

International Journal of Engineering Technologies IJET

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Abstract-Based on the Taylor series expansion (TSE) and employing the technique of differential transform method (DTM), three new meshless approaches which are called Meshless Implementation of Taylor Series Methods (MITSM) are presented. In particular, Strong Form Meshless Implementation of Taylor Series Methods (SMITSM) are studied in this paper. Then, the basic functions are used to solve a 1D second-order ordinary differential equation and 2D Laplace equation by using the SMITSM. Comparisons are made with the analytical solutions and results of Symmetric Smoothed Particle Hydrodynamics (SSPH) method. We also compared the effectiveness of the SMITSM and SSPH method by considering various particle distributions, nonhomogeneous terms and number of terms in the basic functions. It is observed that the MITSM has the conventional convergence properties and, at the expense of CPU time, yields smaller L 2 error norms than the SSPH method, especially in the existence of nonsmooth nonhomogeneous problems.

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“…Some of the fundamental theorems on differential transform can be found in [16][17][18][19][20][21].…”

Section: Differential Transform Methodsmentioning

confidence: 99%

Different Implementation Approaches of the Strong Form Meshless Implementation of Taylor Series Method

Karamanlı¹

2015

International Journal of Engineering Technologies IJET

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“…Let x(t) be analytic function in a field that Taylor series expansion of x(t) is of the form of the following [15].…”

Section: Solution With Differential Transformation Methods (Dtm)mentioning

confidence: 99%

Differential transformation method to determine magneto hydrodynamics flow of compressible fluid in a channel with porous walls

2014

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In this article magneto hydrodynamics (MHD) boundary layer flow of compressible fluid in a channel with porous walls have been researched. In this study it is shown that the nonlinear Navier-Stokes equations can be reduced to an ordinary differential equation, using the similarity transformations and boundary layer approximations. Analytical solution of the developed nonlinear equation is carried out by the Differential Transformation Method (DTM). In addition to applying DTM into the obtained equation, the result of the mentioned method is compared with a type of numerical analysis as Boundary Value Problem method (BVP) and a good agreement is seen. The effects of the Reynolds number and Hartman number are investigated.

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“…It has been used to solve effectively, easily and accurately a large class of linear and nonlinear problems with approximations. The method is well addressed in [9][10][11][12][13][14]. However, DTM has some drawbacks.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Two Forms of Blasius Equation on a Half-Infinite Domain

Ertürk

Momani

2008

Journal of Algorithms & Computational Technology

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A numerical method for solving two forms of Blasius equation is proposed. The Blasius equation is a third order nonlinear ordinary differential equation, which arises in the problem of the two-dimensional laminar viscous flow over a half-infinite domain. The approach is based on differential transform method and Padé approximations. In this scheme, the solution takes the form of a convergent series with easily computable components. The obtained series solution is combined with the diagonal Padé approximations to handle the boundary condition at infinity for only one of these forms. The numerical results demonstrates the validity and applicabilty of the method and a comparison is made with existing results.

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Differential transform method applied to high index differential–algebraic equations

Cited by 75 publications

References 10 publications

Different Implementation Approaches of the Strong Form Meshless Implementation of Taylor Series Method

Different Implementation Approaches of the Strong Form Meshless Implementation of Taylor Series Method

Differential transformation method to determine magneto hydrodynamics flow of compressible fluid in a channel with porous walls

Numerical Solutions of Two Forms of Blasius Equation on a Half-Infinite Domain

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