Adaptive multi-step differential transformation method to solving nonlinear differential equations
TLDR
A comparison between the MsD TM and the adaptive MsDTM reveals that the proposed approach is an efficiency tool for solving the considered equations using fewer time steps.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2012-02-01 and is currently open access. It has received 43 citations till now. The article focuses on the topics: Adaptive algorithm.read more
Citations
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Motion of a spherical particle on a rotating parabola using Lagrangian and high accuracy Multi-step Differential Transformation Method
TL;DR: In this article, a particle's motion on a rotating parabolic surface is introduced through Lagrange equations and is solved by Multi-step Differential Transformation Method (Ms-DTM).
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High accuracy analysis for motion of a spherical particle in plane Couette fluid flow by Multi-step Differential Transformation Method
TL;DR: In this paper, the authors solved the coupled equations of particle motion in Couette fluid flow by Multi-step Differential Transformation Method (Ms-DTM) considering the rotation and shear effects on lift force and neglecting gravity.
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Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM–FDM
TL;DR: In this paper, a zero-equation turbulence model is used to simulate turbulent flow and an analytical procedure is used for finding the effects of the problem parameters on the average Nusselt number over the lower plate depends linearly on volume fraction of nanofluid, Hall parameter, turbulent Eckert number, and Reynolds number.
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Solutions of Sequential Conformable Fractional Differential Equations around an Ordinary Point and Conformable Fractional Hermite Differential Equation
TL;DR: In this article, the authors give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2.
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Applications of Adaptive Multi Step Differential Transform Method to Singular Perturbation Problems Arising in Science and Engineering
TL;DR: In this paper, piecewise-analytical and numerical solutio ns of singular perturbation initial-value problems are obtined by an adaptive multi-step differential transform method (MsDTM).
References
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Book
Theory of sound
TL;DR: In this article, the Laplace's functions of T, F, V are simultaneously reducible to sums of squares, where T is the length of a string, F is the degree of freedom of the string, and V is the size of the chord.
Journal ArticleDOI
Solutions of the system of differential equations by differential transform method
TL;DR: Three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time and exact solutions of linear and non-linear systems of partial differential equations have been investigated.
Journal ArticleDOI
A generalized differential transform method for linear partial differential equations of fractional order
Zaid Odibat,Shaher Momani +1 more
TL;DR: A new generalization of the two-dimensional differential transform method is developed that will extend the application of the method to linear partial differential equations with space- and time-fractional derivatives, generalized Taylor’s formula and Caputo fractional derivative.
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Solution of boundary value problems for integro-differential equations by using differential transform method
Aytac Arikoglu,Ibrahim Ozkol +1 more
TL;DR: The commonly encountered linear and nonlinear integro-differential equations that appear in literature are solved as an illustration for the efficiency of the differential transform method.
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Generalized differential transform method : Application to differential equations of fractional order
TL;DR: A new generalization of the one-dimensional differential transform method that will extend the application of the method to differential equations of fractional order is proposed, based on generalized Taylor’s formula and Caputo fractional derivative.