A finite volume–finite difference method with a stiff ordinary differential equation solver for advection–diffusion–reaction equation

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

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Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4042687 ◽

2019 ◽

Vol 14 (4) ◽

Cited By ~ 14

Author(s):

Anup Singh ◽

S. Das ◽

S. H. Ong ◽

H. Jafari

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Diffusion Equation ◽

Difference Method ◽

Conservative System ◽

Computational Time ◽

Advection Diffusion Equation ◽

Advection Diffusion ◽

Nonlinear Reaction ◽

Sink Term

In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.

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Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences

Mathematics ◽

10.3390/math8020215 ◽

2020 ◽

Vol 8 (2) ◽

pp. 215 ◽

Cited By ~ 3

Author(s):

Alessandra Jannelli

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Fractional Differential Equations ◽

Numerical Solutions ◽

Diffusion Reaction ◽

Unconditionally Stable ◽

Advection Diffusion ◽

Engineering Sciences ◽

Hydrodynamic Processes ◽

Fractional Differential

This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.

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A hybrid immersed boundary-lattice Boltzmann/finite difference method for coupled dynamics of fluid flow, advection, diffusion and adsorption in fractured and porous media

Computers & Geosciences ◽

10.1016/j.cageo.2019.04.005 ◽

2019 ◽

Vol 128 ◽

pp. 70-78 ◽

Cited By ~ 7

Author(s):

Xu Yu ◽

Klaus Regenauer-Lieb ◽

Fang-Bao Tian

Keyword(s):

Porous Media ◽

Fluid Flow ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Lattice Boltzmann ◽

Immersed Boundary ◽

Coupled Dynamics ◽

Advection Diffusion

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Use of Finite Difference Method in the Study of Stepped Beams

International Journal of Mechanical Engineering Education ◽

10.1177/030641909802600103 ◽

1998 ◽

Vol 26 (1) ◽

pp. 11-24 ◽

Cited By ~ 7

Author(s):

A. Krishnan ◽

Geetha George ◽

P. Malathi

Keyword(s):

Differential Equation ◽

Finite Difference ◽

Finite Difference Method ◽

Free Vibration ◽

Difference Method ◽

Geometric Properties ◽

Stepped Beam

The analysis of stepped beams using finite difference method normally is carried by use of a single differential equation. Whenever the step is a node, numerical values of average geometric properties are taken for computation. It is expected that, with finer meshes, the solution will converge to an acceptable one. Free vibration studies carried out on a stepped beam do not confirm this expectation. The numerical values converge; but to wrong ones. Some details are presented in this paper.

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