This article deals with the unsteady flow in rotating circular plates located at a finite distance filled Reiner-Rivlin nanofluid. The nanofluid is electrically conducting and incompressible. Furthermore, also accommodates motile gyrotactic microorganisms under effect of activation energy thermal radiation. mathematical formulation performed by employing transformation variables. finalized form...

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tan...

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comp...

Differential-algebraic equations (DAEs) are important tools to model complex problems in various application fields easily. Those DAEs with an index-3, even the linear ones, known cause when solving them numerically. The present article proposes a new algorithm together its multistage form efficiently solve class of nonlinear implicit Hessenberg index-3 DAEs. This is based on idea applying diff...

This study investigates the use of differential transform method (DTM) for integrating Rössler system fractional order. Preliminary studies integer-order system, with reference to other well-established integration methods, made it possible assess quality and determine optimal parameter values that should be used when a different dynamic characteristics. Bifurcation diagrams obtained show that,...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

In this paper, an analytic solution is presented using differential transform method (DTM) for a class of wave equation. The emphasis is on the nonlinear two-dimensional wave equation. The procedures introduced in this paper are in recursive forms which can be used to obtain the closed form of the solutions, if they are required. The method is tested on various examples, and the results reveal ...

In this paper, Least Square Method (LSM) and Differential Transformation Method (DTM) are used to solve the problem of laminar nanofluid flow in a semi-porous channel in the presence of transverse magnetic field. Due to existence some shortcomings in each method, a novel and efficient method named LS-DTM is introduced which omitted those defects and has an excellent agreement with numerical sol...

In this study, a reliable algorithm to develop approximate solutions for the problem of fluid flow over a stretching or shrinking sheet is proposed. It is depicted that the differential transform method (DTM) solutions are only valid for small values of the independent variable. The DTM solutions diverge for some differential equations that extremely have nonlinear behaviors or have boundary-co...