Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet scheme for solving the 2D Bratu problem

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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“…Substituting Eqs. (24) and (27) into Eq. (25), we arrive at the autonomous Ginzburg-Landau equation in the form:…”

Section: Weakly Nonlinear Analysismentioning

confidence: 99%

“…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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“…In [11][12][13][14][15][16][17][18] introduced Bernstein, several methods for numerical solutions of VIDE form the unique Emden-Fowler initial value problems. In [19] approach developed to obtain analytical-numerical solutions to two separate Lane-Emden problems. In [20][21][22][23][24] introduced the exponential transformation to resolve the difficulty of a singular point to solve the LEE.…”

Section: Function Approximation By the Hobw Functionsmentioning

confidence: 99%

A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

Ali

2019

SN Appl. Sci.

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Hybrid orthonormal Bernstein and block-pulse function wavelet method for many phenomena in mathematical physics and astrophysics is considered. We use a fundamental administrator and convert Lane-Emden conditions into necessary conditions. The upsides of utilizing the proposed strategy are introduced. At that point, an effective error estimation for the proposed technique is additionally presented lastly a few examinations and their numerical arrangements are given; and looking at between the numerical outcomes acquired from alternate strategies, we demonstrate the high exactness and productivity of the proposed strategy. Our method is characterized then the singular equations are transformed to Volterra integro-differential equations. We modify this equations to an algebraic system of equations. The solution to this application is achieved by solving this system and the constructed solutions are on approximation form. The acquired results guarantee the method provides a truncate solution to the Lane-Emden equations.

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“…Bilinear technique is a powerful representative calculation to develop 2 Advances in Mathematical Physics numerous solitons. Very as of late, Ma et al stretched out this technique to look for lump arrangements, where its basic thought is to pick appropriate polynomial capacities in bilinear frames [30][31][32][33][34][35][36][37][38]. We are roused to investigate new dynamical properties through examining irregularity answer for nonlinear frameworks.…”

Section: Introductionmentioning

confidence: 99%

New Exact Solutions of Nonlinear (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation

Ali

2019

Advances in Mathematical Physics

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Based on Hirota’s bilinear structure, we evolute a new protuberance type arrangement of the (3+1)-dimensional Boiti-Boiti-Leon-Manna-Pempinelli equation, which depicts nonlinear wave spreads in incompressible fluid. New lump arrangement is built by applying the bilinear strategy and picking appropriate polynomial. Under various parameter settings, this lump arrangement has three sorts of numerous irregularity waves, blended arrangements including lump waves and solitons are additionally developed. Association practices are seen between lump soliton and soliton. Research demonstrates that soliton can somewhat swallow or release lump waves. The shape and highlights for these subsequent arrangements are portrayed by exploiting the three-dimensional plots and comparing shape plots by picking suitable parameters. The physical significance of these charts is given.

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Hybrid Orthonormal Bernstein and Block-Pulse functions wavelet scheme for solving the 2D Bratu problem

Cited by 38 publications

References 20 publications

Convection in a horizontal layer of water with three diffusing components

Convection in a horizontal layer of water with three diffusing components

A new algorithm for solving the nonlinear Lane–Emden equations arising in astrophysics

New Exact Solutions of Nonlinear (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation

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