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We study the inviscid Burgers equation which models nonlinear wave propagation. We derive the inviscid Burgers equation from the Navier-Stokes equation and solve it using the Adomian decomposition method. By means of numerical exa...
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We study the inviscid Burgers equation which models nonlinear wave propagation. We derive the inviscid Burgers equation from the Navier-Stokes equation and solve it using the Adomian decomposition method. By means of numerical examples we show that the Adomian decomposition method produces results that compare favourably with the exact solution obtained using the method of characteristics.
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We consider coupled systems of advection-diffusion equations with initial and boundary conditions and determine conditions on the advection terms that allow us to obtain solutions that can be explicitly bounded above and below usi...
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We consider coupled systems of advection-diffusion equations with initial and boundary conditions and determine conditions on the advection terms that allow us to obtain solutions that can be explicitly bounded above and below using the initial and boundary conditions. Given the advection terms, using our methodology one can easily check if such bounds can be obtained and then one can construct the necessary nonlinear transformation to allow the bounds to be determined. We apply this technique to determine bounding quantities for a number of examples. In particular, we show that the three-ion electroneutral Poisson-Nernst-Planck system of equations can be transformed into a system, which allows for the use of our techniques and we determine the bounding quantities. In addition, we determine the general form of advection terms that allow these techniques to be applied and show that our method can be applied to a very wide class of advection-diffusion equations.
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This paper is concerned with numerical solution ofcoupled Burgers’ equation by the combination of finite difference and sinc collocation method. Firstly, we derive the semidiscrete scheme by approximating the first order derivati...
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This paper is concerned with numerical solution ofcoupled Burgers’ equation by the combination of finite difference and sinc collocation method. Firstly, we derive the semidiscrete scheme by approximating the first order derivative oftime with θ-weighted scheme. Different schemes can be obtainedby selecting different values of θ. After that, a fully discretescheme is constructed through the use of sinc collocation andfinite difference method to approximate the first and secondorder derivatives of space. The stability of the fully discretescheme is analyzed by representing the proposed scheme inmatrix form. For Burgers’ equation, the similar results couldbe obtained. At last, some numerical examples are presented toillustrate the efficiency and superiority of present method forsolving Burgers’ and coupled Burgers’ equation.
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Obtaining the numerical approximation of fractional partial differential equations (PDEs) is a cumbersome task. Therefore, more researchers regarding approximated-analytical solutions of such complex-natured fractional PDEs (FPDEs...
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Obtaining the numerical approximation of fractional partial differential equations (PDEs) is a cumbersome task. Therefore, more researchers regarding approximated-analytical solutions of such complex-natured fractional PDEs (FPDEs) are required. In this article, analytical-approximated solutions of the fractional-order coupled Burgers’ equation are provided in one-, two-, and three-dimensions. The proposed technique is named as Iterative Shehu Transform Method (ISTM). The simplicity and accurateness of the method are affirmed through five examples. Graphical representation and tabular discussion are provided to compare the exact and approximated results. The robustness of the proposed regime is also validated by error analysis. In the present work, approximated and exact solutions are compared to verify the validity of the proposed scheme. Error analysis is also provided through which the efficiency of the proposed scheme can be assured. Obtained errors are lesser than the compared results.
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Previous studies dealing with plant-based meat analogs confirmed the potential of oral processing methods to identify options for improving those products. Knowing that sensory perception can be influenced by adding condiments, th...
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Previous studies dealing with plant-based meat analogs confirmed the potential of oral processing methods to identify options for improving those products. Knowing that sensory perception can be influenced by adding condiments, this short communication aimed to investigate the texture and oral processing of four plant-based burger analogs and a beef burger when consumed in portions or as part of model meals with buns and sides. Texture profile analysis indicated that beef burgers and analog E were the toughest. Two analogs (B and S) showed textures close to beef, while one (analog D) displayed significantly lower values for hardness, toughness, cohesiveness, and springiness. The instrumental data was only partly reflected in the mastication parameters. Adaptations in mastication behavior were expected, but differences between the plant-based analogs were smaller than anticipated, although clear differences were observed for consumption time, number of chews and number of swallows. On the whole, mastication patterns concurred within different consumption scenarios (portions, model burgers), and significant correlations with instrumental texture were obtained.
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In this research, the He's variational iteration technique is used for computing an unknown time-dependent parameter in an inverse quasilinear parabolic partial differential equation. Parabolic partial differential equations with ...
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In this research, the He's variational iteration technique is used for computing an unknown time-dependent parameter in an inverse quasilinear parabolic partial differential equation. Parabolic partial differential equations with over-specified data play a crucial role in applied mathematics and physics, as they appear in various engineering models. The He's variational iteration method is an analytical procedure for finding solutions of differential equations, is based on the use of Lagrange multipliers for identification of an optimal value of a parameter in a functional. To show the efficiency of the new approach, several test problems are presented for one-, two- and three-dimensional cases. (C) 2006 Elsevier Ltd. All rights reserved.
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A family {q} of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations. It is shown that the functions q(n) from {q} for some n = 2,4,... are clo...
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A family {q} of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations. It is shown that the functions q(n) from {q} for some n = 2,4,... are closely related to the special unitary groups SU(n). The necessary and sufficient conditions for existence of a family of the exact multicomponent travelling wave solutions to a quasilinear evolution equation are given. An efficiency of the method based on q-functions is demonstrated on several classes of the nonlinear partial differential equations. (C) 1997 American Institute of Physics. [References: 17]
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We construct 2N real parameter solutions to the Burgers’ equation in terms of determinant of order N and we call these solutions, N order solutions. We deduce general expressions of these solutions in terms of exponentials and st...
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We construct 2N real parameter solutions to the Burgers’ equation in terms of determinant of order N and we call these solutions, N order solutions. We deduce general expressions of these solutions in terms of exponentials and study the patterns of these solutions in functions of the parameters for N = 1 until N = 4.
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The dislocation density tensor at the macroscale may be obtained by using two seemingly disparate definitions given by Nye and Arsenlis and Parks. Nye’s definition depends on counting the dislocations crossing a Burgers circuit o...
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The dislocation density tensor at the macroscale may be obtained by using two seemingly disparate definitions given by Nye and Arsenlis and Parks. Nye’s definition depends on counting the dislocations crossing a Burgers circuit of infinitesimal area at the macroscale, where as Arsenlis and Parks’s definition is defined as an integrated property of dislocations within an infinitesimal volume. In this paper, it is shown that Arsenlis and Parks’ and Nye’s definitions for the dislocation density tensor are equivalent when conditions on the length scales of the spacing and curvature of the dislocation lines are obeyed. It is also shown that the definition by Arsenlis and Parks, which can be easily employed in microscopic dislocation dynamics simulations, follows the fundamental extensive property of the Burgers vector, namely, the total Burgers vector of a Burgers circuit is the sum of Burgers vectors of individual dislocation lines intersecting the circuit.
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In this paper, solutions of generalized Burger’s–Huxley equation and Burgers equation are proposed through a numerical method. The method is developed by using CAS wavelet in conjunction with Picard technique. Operational matric...
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In this paper, solutions of generalized Burger’s–Huxley equation and Burgers equation are proposed through a numerical method. The method is developed by using CAS wavelet in conjunction with Picard technique. Operational matrices for CAS wavelet are derived and constructed. The implementation procedure is provided. Error analysis and convergence of presentmethod is also presented. The results of the CASwavelet Picardmethod are compared with results from some well known methods which support the accuracy, efficiency and validity of the CAS wavelet Picard scheme.
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