scholarly journals A new computational for approximate analytical solutions of nonlinear time-fractional wave-like equations with variable coefficients

2020 ◽  
Vol 5 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Ali Khalouta ◽  
◽  
Abdelouahab Kadem
Keyword(s):  
Analytical Solutions ◽  
Variable Coefficients ◽  
Approximate Analytical Solutions

scholarly journals A Homotopy-Analysis Approach for Nonlinear Wave-Like Equations with Variable Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Afgan Aslanov
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Equations ◽  
Nonlinear Wave ◽  
Analytical Solutions ◽  
Wave Operator ◽  
Series Solution ◽  
Variable Coefficients ◽  
Analysis Approach ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

We are interested in the approximate analytical solutions of the wave-like nonlinear equations with variable coefficients. We use a wave operator, which provides a convenient way of controlling all initial and boundary conditions. The proposed choice of the auxiliary operator helps to find the approximate series solution without any discretization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method.

Approximate analytical solutions of stability problems for skew plates under combined loading

2011 ◽  
Vol 54 (2) ◽  
pp. 115-124 ◽  
Author(s):  
N. I. Akishev ◽  
I. I. Zakirov ◽  
V. A. Ivanov ◽  
V. N. Paimushin ◽  
M. A. Shishov
Keyword(s):  
Analytical Solutions ◽  
Combined Loading ◽  
Stability Problems ◽  
Approximate Analytical Solutions

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

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