A Note on the Stability of the Integral-Differential Equation of the Parabolic Type

2011 ◽  
Author(s):  
Maksat Ashyraliyev ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Differential Equation ◽  
Parabolic Type ◽  
The Stability ◽  
Integral Differential Equation

scholarly journals A Note on the Stability of the Integral-Differential Equation of the Parabolic Type in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Difference Scheme ◽  
Unique Solvability ◽  
Parabolic Type ◽  
Stability Estimates ◽  
The Difference ◽  
The Stability ◽  
Integral Differential Equation

The integral-differential equation of the parabolic type in a Banach space is considered. The unique solvability of this equation is established. The stability estimates for the solution of this equation are obtained. The difference scheme approximately solving this equation is presented. The stability estimates for the solution of this difference scheme are obtained.

scholarly journals On Gronwall’s type integral inequalities with singular kernels

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1041-1049 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Fractional Differential Equations ◽  
Parabolic Type ◽  
Integral Inequalities ◽  
Stability Estimates ◽  
Type Integral ◽  
Singular Kernels ◽  
Fractional Differential ◽  
Integral Differential Equation

In this paper, the generalizations of Gronwall?s type integral inequalities with singular kernels are established. In applications, theorems on stability estimates for the solutions of the nonliner integral equation and the integral-differential equation of the parabolic type are presented. Moreover, these inequalities can be used in the theory of fractional differential equations.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

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