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Analysis of a finite-difference method Based on Nonlocal Approximations for a Nonlinear, Extended Three-Compartmental Model of Ethanol Metabolism in the Human Body

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MATHEMATICAL methodS IN THE APPLIED SCIENCES 2025年第9期48卷 9975-9992页

作者： Wacker, Benjamin Univ Appl Sci Merseburg Dept Engn & Nat Sci Merseburg Germany

In this work, we combine two different existing two-compartmental models of ethanol metabolism and propose a nonlinear three-compartmental model of ethanol metabolism in the human body based on Michaelis-Menten kinetics for elimination of ethanol in liver cells. Hence, we obtain a system of nonlinear differential equations, which describes the approximate dynamics of ethanol elimination in the human body. Furthermore, we show that our time-continuous model possesses a unique nonnegative solution globally in time and has exactly one stable fixed point whose stability is shown. Afterward, we suggest a nonstandard finite-difference method based on Mickens' methodology for its numerical solution and examine all properties of our time-continuous model, which are preserved in the time-discrete case. Additionally, we show that the proposed scheme converges linearly towards the solution of the time-continuous model. Conclusively, we underline our theoretical findings by numerical examples.

关键词： convergence dynamical systems equilibrium state existence finite-difference method nonlocal approximations numerical analysis uniqueness

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Solving the relativistic Hartree-Bogoliubov equation with the finite-difference method

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Chinese Physics C 2025年第1期49卷 245-254页

作者： Yiran Wang Xiaojie Cao Jinniu Hu Ying Zhang Department of Physics Faculty of ScienceTianjin UniversityTianjin 300354China School of Physics Nankai UniversityTianjin 300071China

The relativistic Hartree-Bogoliubov(RHB)theory is a powerful tool for describing exotic nuclei near drip *** key technique is to solve the RHB equation in the coordinate space to obtain the quasi-particle *** this paper,we solve the RHB equation with the Woods-Saxon-type mean-field and Delta-type pairing-field potentials by using the finite-difference method(FDM).We inevitably obtain spurious states when using the common symmetric central difference formula(CDF)to construct the Hamiltonian matrix,which is similar to the problem resulting from solving the Dirac equation with the same *** problem is solved by using the asymmetric difference formula(ADF).In addition,we show that a large enough box is necessary to describe the continuum quasi-particle *** canonical states obtained by diagonalizing the density matrix constructed by the quasi-particle states are not particularly sensitive to the box *** of the asymptotic wave functions can be improved by applying the ADF in the FDM compared to the shooting method with the same box boundary condition.

关键词： relativistic Hartree-Bogoliubov equation spurious state finite-difference method

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finite-difference method for the Navier-Stokes Equations in a Variable Domain with Curved Boundaries

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第3期48卷 464-476页

作者： Usov, A. B. So Fed Univ Rostov Na Donu 334090 Russia

A semi-implicit finite-difference scheme is proposed for solving the nonlinear viscous compressible Navier-Stokes equations. Coordinate transformations are constructed that yield a uniform mesh in the computational plane even though the physical domain under consideration is time-varying and curvilinear. The finite-difference scheme was tested using model examples.

关键词： finite-difference method Navier-Stokes equations semi-implicit finite-difference scheme splitting method

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A finite-difference method for the Falkner-Skan equation

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APPLIED MATHEMATICS AND COMPUTATION 1998年第2-3期92卷 135-141页

作者： Asaithambi, A St Louis Univ Parks Coll Engn & Aviat Dept Sci & Math St Louis MO 63156 USA

We present a finite-difference method for the solution of the Falkner-Skan equation. The method uses a coordinate transformation to map a semi-infinite physical domain to the unit interval [0, 1]. After using a suitable change of variables, the transformed third order boundary value problem for this domain is solved using a finite-difference scheme. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors. (C) 1998 Published by Elsevier Science Inc. All rights reserved.

关键词： Falkner-Skan equation finite-difference method coordinate transformation third-order two-point boundary value problem nonlinear system of algebraic equations tridiagonal Jacobian matrix

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finite-difference method for fuzzy singular integro-differential equation deriving from fuzzy non-linear differential equation

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GRANULAR COMPUTING 2023年第3期8卷 503-524页

作者： Moi, Sandip Biswas, Suvankar Sarkar, Smita Pal Indian Inst Engn Sci & Technol Dept Math Howrah 711103 India Indira Gandhi Natl Open Univ Sch Sci Discipline Math New Delhi 110068 India

In this article, first time, a well-known equation, which can be used to analyze the behavior of the bubble formulation in the mixture of gas and liquid in fluid dynamics, has been considered in the form of a non-linear ordinary differential equation in fuzzy environment. In addition, the fuzzy non-linear ordinary differential equation has been presented in the sense of acut. Then, the left and right branches of ordinary differential equations have been converted into Volterra integro-differential equations with singular kernels. A numerical method based on the numerical approximation of first-order derivative by finite difference has been modified to solve the equation after converting it into the non-linear singular integro-differential equations. In the first-order method, the right rectangles rules have been used to compute the integrals in the converted equations. In addition, in the second-order method, the integrals have been analyzed with the help of trapezoidal rule instead of right rectangles rule. After that, the iterative sequence has been defined to find the approximate solution of the given equation for both first- and second-order methods. A convergence analysis has been developed for both first- and second-order methods in the form of different types of lemmas and theorems for different cases. Some of these theorems have been shown that the equations are uniquely solvable for both first- and second-order methods. These results have been shown with the help of Banach fixed-point theorem. A brief comparison of our method with other existing methods has been presented to show the efficiency and reliability of our proposed method. In addition, a brief discussion about the advantages and disadvantages of our method has been discussed. Some numerical examples have been chosen and examined to show the validation of our proposed method. In addition, some error analysis have been examined in the form of different types of tables and figures which shows the ef

关键词： Fuzzy derivative Fuzzy integration Fuzzy boundary value problem Fuzzy integro-differential equation finite-difference method

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finite-difference method of order six for the two-dimensional steady and unsteady boundary-layer equations

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2005年第5期16卷 757-780页

作者： Salama, AA Mansour, AA Assiut Univ Fac Sci Dept Math Assiut 71516 Egypt Al Azhar Univ Fac Sci Dept Math Assiut Egypt

In this article, we propose a high order method for solving steady and unsteady two-dimensional laminar boundary-layer equations. This method is convergent of sixth-order of accuracy. It is shown that this method is unconditionally stable. The unsteady separated stagnation point flow, the Falkner-Skan equation and Blasius equation are considered as special cases of these equations. Numerical experiments are given to illustrate our method and its convergence.

关键词： finite-difference method third-order boundary-value problems stagnation point Falkner-Skan equation Blasius equation

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Analysis of the buckling of rectangular nanoplates by use of finite-difference method

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MECCANICA 2014年第6期49卷 1443-1455页

作者： Ravari, M. R. Karamooz Talebi, S. Shahidi, A. R. Isfahan Univ Technol Dept Mech Engn Esfahan *** Iran

In recent years nanostructures have been widely used in industry, for example in nanoelectromechanical systems (NEMS);knowledge of the mechanical behavior of nanostructured materials is therefore important. In the work discussed in this paper, the non-dimensional buckling load of rectangular nano-plates was determined for general boundary conditions. Non-local theory was used to derive the governing equation, and this equation was then solved, by use of the finite-difference method, by applying different combinations of boundary conditions. To verify the proposed method, the non-dimensional buckling load determined for a simply supported plate was compared with results obtained by use of local theory and with results reported in the literature. When the method was used to calculate the buckling load of nano-beams, results were in good agreement with literature results. As a novel contribution of the work, non-symmetric boundary conditions were also studied. The non-dimensional buckling load was obtained for several values of aspect ratio, non-local variables, and different types of boundary condition. For better understanding, mode shapes are also depicted. The finite-difference method could be a powerful means of determination of the mechanical behavior of nanostructures, with little computational effort, and the results could be as reliable as those obtained by use of other methods. The ability to deal with a combination of boundary conditions illustrates the advantages of this method compared with other methods.

关键词： Nanoplate Buckling load finite-difference method Non-local elasticity theory Rectangular plates

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Investigation of Strain Rate Effects on the Dynamic Response of a Glass/Epoxy Composite Plate Under Blast Loading by Using the finite-difference method

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MECHANICS OF COMPOSITE MATERIALS 2014年第3期50卷 295-310页

作者： Shokrieh, M. M. Karamnejad, A. Iran Univ Sci & Technol Sch Mech Engn Ctr Excellence Expt Solid Mech & Dynam Composites Res Lab Tehran *** Iran

Nonlinear equations of motion for a laminated composite plate under blast loading, based on the first-order shear deformation theory, are derived. The governing equations are solved by the finite-difference method in conjunction with the Newmark time integration scheme. The rules of material property degradation are modified to allow for strain rate effects. A progressive damage model is developed based on the modified rules of material property degradation and Hashin-type failure criteria to predict different failure modes. The validity of the method is demonstrated by quantitative and qualitative comparisons of present results with those available in the literature. Results for clamped glass/epoxy laminated composite plates with constant and strain-rate-dependent mechanical properties under a blast load are presented and compared for various ply stacking sequences, and pertinent conclusions are outlined.

关键词： dynamic response finite-difference method progressive damage model strain rate

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On the accuracy of the Complex-Step-finite-difference method

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 340卷 390-403页

作者： Abreu, Rafael Su, Zeming Kamm, Jochen Gao, Jinghuai Westfalische Wilhelms Univ Munster Inst Geophys Corrensstr 24 D-48149 Munster Germany Univ Granada Inst Andaluz Geofis Campus Cartuja S-N E-18071 Granada Spain Xi An Jiao Tong Univ Xian Shaanxi Peoples R China

The Complex-Step-finite-difference method (CSFDM) is a very simple methodology that can be implemented in well known numerical techniques helping to improve, for instance in the wave propagation problem, time and/or space derivative based wavefields. We clarify differences between the CSFDM and previous implementations of the Complex-Step (CS) derivative approximation in well known numerical techniques. We study dispersion properties for the one-way and two-way wave equations using the finite-difference method (FDM), the Pseudospectral method (PSM), the finite-Element method (FEM) and the CSFDM, under the influence of a plane wave and Ricker source time functions. We show the gain in numerical accuracy offered by the methodology of the CSFDM over the FDM, PSM and FEM. We finally discuss consequences of the CSFDM in future scenarios and propose directions of study in this area. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Numerical solution Wave propagation finite-difference method finite-element method Complex-step method Complex-step-finite-difference method

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A parametric finite-difference method for shallow sea waves

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN FLUIDS 2007年第1期53卷 129-147页

作者： Bratsos, A. G. Famelis, I. Th. Prospathopoulos, A. M. TEI Athens Dept Math GR-12210 Athens Greece Inst Oceanog HCMR GR-19013 Anavyssos Greece

This paper presents a parametric finite-difference scheme concerning the numerical solution of the one-dimensional Boussinesq-type set of equations, as they were introduced by Peregrine (J. Fluid Mech. 1967;27(4)) in the case of waves relatively long with small amplitudes in water of varying depth. The proposed method, which can be considered as a generalization of the Crank-Nickolson method, aims to investigate alternative approaches in order to improve the accuracy of analogous methods known from bibliography. The resulting linear finite-difference scheme, which is analysed for stability using the Fourier method, has been applied successfully to a problem used by Beji and Battjes (Coastal Eng. 1994;23: 1-16), giving numerical results which are in good agreement with the corresponding results given by MIKE 21 BW (User Guide. In: MIKE 21, Wave Modelling, User Guide. 2002;271-392) developed by DHI Software. Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： shallow water waves Boussinesq equations numerical modelling finite-difference method

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