Haar wavelets scheme for solving the unsteady gas-flow in 4-D

Ali, Mohamed R.; Băleanu, Dumitru

doi:10.2298/tsci190101292a

Cited by 19 publications

(12 citation statements)

References 16 publications

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“…In this paper the obtained Ginzburg-Landau equation is tractable and hence an analytical solution is found. Alternately, one can use the HOBW method/Haar wavelet method used by Ali et al [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Convection in a horizontal layer of water with three diffusing components

et al. 2020

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Triple diffusive convection in water is modelled with properties like density, specific heat, thermal conductivity, thermal diffusivity and thermal expansion, modified in the presence of salts. The Ginzburg-Landau equation is derived to study heat and mass transports of different combinations of salts in water. A table is prepared documenting the actual values of thermophysical properties of water with different salts and the critical Rayleigh number is calculated. This information is used in the estimation of Nusselt and Sherwood numbers and their relative magnitudes are commented upon. A detailed study on different single, double and triple diffusive systems is done and comparison is made of the results. The local nonlinear stability analysis made via a Ginzburg-Landau model mimics many properties of the original governing equations, namely, Hamiltonian character and a bounded solution.

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Section: Introductionmentioning

confidence: 99%

Convection in a horizontal layer of water with three diffusing components

et al. 2020

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“…Substituting 7and (8) into (16) and equaling coefficients in derivatives for x and power of u to zero, the system of equations is obtained: α 1 xt − η tψ � 0.…”

Section: Lie Symmetry and Reduction Of Fbbm Equationmentioning

confidence: 99%

“…Partial differential equations running into the thinking of most of the researchers as it represented the importance in several topics of scientific fields as mechanics, optical fibers, medical sciences (as breast cancer), biological science, turbulent bursts, and oceans waves [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for Nonlinear Dispersive Physical Model

Ali

Sadat

2020

Complexity

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Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.

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“…Nazari and Darvishi [11] gave a two dimensional Haar wavelets method for solving system of PDEs. Ali and Baleanu [12] used Haar wavelets for the solution of the problem of unsteady gas flow in four-dimensional. Ali [13] gave the truncation method for solving the time-fractional Benjamin-Ono equation.…”

Section: Introductionmentioning

confidence: 99%

Duality relations of Kamal transform with Laplace, Laplace–Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms

Aggarwal¹,

Sharma

Chauhan

2019

SN Appl. Sci.

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Integral transforms have wide applications in the various disciplines of engineering and science to solve the problems of heat transfer, springs, mixing problems, electrical networks, bending of beams, carbon dating problems, Newton's second law of motion, signal processing, exponential growth and decay problems. In this paper, authors discussed the duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms. Tabular presentation of Laplace transform, Laplace-Carson transforms, Aboodh transform, Sumudu transform, Elzaki transform, Mohand transform and Sawi transform of mostly used basic mathematical functions are given to visualize the importance of duality relations of Kamal transform with Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms. To show the practical importance of the paper, a problem of the field of pharmacokinetics has been taken and solved in full steps using Kamal transform with the help of mention duality relations. Results show that Kamal transform and Laplace, Laplace-Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms have a strong relationship.

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Haar wavelets scheme for solving the unsteady gas-flow in 4-D

Cited by 19 publications

References 16 publications

Convection in a horizontal layer of water with three diffusing components

Convection in a horizontal layer of water with three diffusing components

Analytical Solutions for Nonlinear Dispersive Physical Model

Duality relations of Kamal transform with Laplace, Laplace–Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms

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