scholarly journals Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method

2016 ◽  
Vol 06 (04) ◽  
pp. 287-297 ◽  
Author(s):  
Ayad R. Khudair ◽  
S. A. M. Haddad ◽  
Sanaa L. Khalaf
Keyword(s):  
Differential Equations ◽  
Transformation Method ◽  
Second Order ◽  
Differential Transformation Method ◽  
Mean Square ◽  
Differential Transformation ◽  
Random Differential Equations

Differential Transformation Method for the Flow and Heat Transfer Due to a Permeable Stretching Surface Embedded in a Porous Medium With a Second Order Slip and Viscous Dissipation

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
M. M. Khader ◽  
Ahmed M. Megahed
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Transformation Method ◽  
Second Order ◽  
Differential Transformation Method ◽  
Stretching Surface ◽  
Local Skin ◽  
Differential Transformation

This paper is devoted to introduce a numerical simulation using the differential transformation method (DTM) with a theoretical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second order slip. The governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations (ODEs) by using similarity variables. The resulting ODEs are successfully solved numerically with the help of DTM. Graphic results are shown for nondimensional velocities and temperatures. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first and second order velocity slip parameters and the Prandtl number on the flow and temperature profiles are given. Moreover, the local skin-friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

scholarly journals Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 231 ◽  
Author(s):  
Nadeem Salamat ◽  
Muhammad Mustahsan ◽  
Malik Saad Missen
Keyword(s):  
Differential Equations ◽  
Numerical Technique ◽  
Transformation Method ◽  
Higher Order ◽  
Differential Transformation Method ◽  
Fuzzy Differential Equation ◽  
Differential Transformation ◽  
Point Solution ◽  
Definition Of ◽  
Higher Order Differential Equations

The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations.

Generalized Differential Transformation Method for Solving system of Non linear Volterra integro-differential equations of fractional order

2018 ◽  
Vol 1 (25) ◽  
pp. 523-550
Author(s):  
Basim N.Abood ◽  
Eman A.Hussain ◽  
Mayada T. Wazi
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Differential Transformation ◽  
Modified Method ◽  
Non Linear ◽  
Generalized Differential

       In this paper,  the technique of modified Generalized  Differential Transformation Method (GDTM)  is used to solve a system of Non linear integro-differential equations with initial conditions. Moreover, a particular example has been discussed in three different cases to show reliability and the performance of the modified   method. The fractional derivative is considered in the Caputo sense .The approximate solutions are calculated in the form of a convergent series, numerical results explain that this approach is trouble-free to put into practice and correct when applied to systems integro-differential equations.

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