scholarly journals On a New Integral Transform and Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
A. Kiliçman ◽  
H. Eltayeb
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Transform ◽  
System Of Differential Equations ◽  
Transform Method ◽  
Control Engineering ◽  
Linear Ordinary Differential Equations ◽  
Sumudu Transform ◽  
Integral Transform Method

Integral transform method is widely used to solve the several differential equations with the initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform was introduced as a new integral transform by Watugala to solve some ordinary differential equations in control engineering. Later, it was proved that Sumudu transform has very special and useful properties. In this paper we study this interesting integral transform and its efficiency in solving the linear ordinary differential equations with constant and nonconstant coefficients as well as system of differential equations.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

A NEW INTEGRAL TRANSFORM METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 102 (12) ◽  
pp. 2913-2940
Author(s):  
Bhausaheb R. Sontakke ◽  
Govind P. Kamble ◽  
Suvarna R. Acharya
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Transform ◽  
Transform Method ◽  
Fractional Differential ◽  
Integral Transform Method

FORCES, MOMENTS, ROTATIONS, AND DISPLACEMENTS OF POLYNOMIAL-SHAPED CURVED BEAMS

2010 ◽  
Vol 10 (01) ◽  
pp. 77-89 ◽  
Author(s):  
LAZARO GIMENA ◽  
PEDRO GONZAGA ◽  
FAUSTINO GIMENA
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Mechanical Behavior ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
The Other ◽  
Curved Beams ◽  
Fourth Degree ◽  
Linear Ordinary Differential Equations ◽  
Parabolic Shape

This paper deals with curved beams with polynomial free geometry. The problem is approached analytically and the differential equations that govern the mechanical behavior of curved beams are presented. A system of twelve linear ordinary differential equations is solved using either an analytical or a customized numerical method with boundary conditions. Results of the different components of forces, moments, rotations, and displacements are given and plotted in the examples for different polynomial-shaped beams of the fourth degree. It is concluded from the present analyses that the parabolic shape has better response to distributed loads than the other polynomial-shaped beams considered.

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