In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black–Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed ...

In this study, flapwise bending vibration analysis of a tapered Timoshenko beam mounted on the periphery of a rotating rigid hub is performed. The governing differential equations of motion for pure bending are derived using the Hamilton’s principle and solved using the Differential Transform Method, DTM. During the derivation of the equations, effects of rotary inertia, shear deformation and h...

This paper proposes a new semi-analytical approach for online time-domain power system simulation. The approach applies the differential transformation method (DTM) to the power system differential equation model to offline derive a semi-analytical solution (SAS) having symbolic variables about time, the initial state and system conditions. When simulation is online needed for a contingency und...

The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

Three different profiles of the straight fin that has a temperature-dependent thermal conductivity are investigated by differential transformation method DTM and compared with numerical solution. Fin profiles are rectangular, convex, and exponential. For validation of the DTM, the heat equation is solved numerically by the fourth-order Runge-Kutta method. The temperature distribution, fin effic...

and Applied Analysis 3 Table 1: Operations of the two-dimensional differential transform. Original function Transformed function u x, y f x, y ∓ g x, y Uα,β k, h Fα,β k, h ∓G k, h u x, y ξf x, y Uα,β k, h ξFα,β k, h u x, y ∂f x, y /∂x Uα,β k, h k 1 F k 1, h u x, y D ∗x0f x, y , 0 < α ≤ 1 Uα,β k, h Γ α k 1 1 /Γ αk 1 Fα,β k 1, h u x, y D ∗y0f x, y , 0 < α ≤ 1 Uα,β k, h Γ α h 1 1 /Γ αh 1 Fα,β k, h...

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the differential transform method (DTM). Graphical results are presented to investigate the influence of the non-dimensional wall dilati...