The equimaterial approach for the numerical solution of the one dimensional transient diffusion equation with zero flux boundary conditions

2011 ◽  
Vol 218 (4) ◽  
pp. 1353-1359
Author(s):  
M. Kostoglou
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
One Dimensional ◽  
Transient Diffusion ◽  
Flux Boundary Conditions ◽  
The One

Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

2018 ◽  
Vol 284 ◽  
pp. 1230-1234
Author(s):  
Mikhail V. Maisuradze ◽  
Alexandra A. Kuklina
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Differential Diffusion ◽  
One Dimensional ◽  
The Third ◽  
Dimensional Diffusion ◽  
Simplified Algorithm ◽  
The One ◽  
Carburizing Process ◽  
Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

scholarly journals On the numerical solution of the one-dimensional convection-diffusion equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The One

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.

NUMERICAL ANALYSIS OF FINITE DEPTH PROBLEMS IN SOIL-WATER HYDROLOGY

1971 ◽  
Vol 2 (1) ◽  
pp. 1-22 ◽  
Author(s):  
K. K. WATSON
Keyword(s):  
Numerical Analysis ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Soil Water ◽  
Water Table ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Flow Equation ◽  
One Dimensional ◽  
The One

The types of initial and boundary conditions which may be involved in the flow of water through an unsaturated profile to a water table are discussed. A numerical solution of the flow equation is then outlined and its use in the one-dimensional drainage of a homogeneous profile and in ponded infiltration into a draining profile detailed. Several characteristics of the drainage of deep profiles are discussed together with numerical solutions for the drainage of a stratified profile and infiltration into a draining profile.

The Effect of Spacewise Lumping on the Solution Accuracy of the One-Dimensional Diffusion Equation

1962 ◽  
Vol 29 (4) ◽  
pp. 629-636 ◽  
Author(s):  
W. D. Murray ◽  
Fred Landis
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
One Dimensional ◽  
Truncation Errors ◽  
Dimensional Diffusion ◽  
Temperature Boundary ◽  
The Laplace Transform ◽  
The One ◽  
Solution Accuracy ◽  
General Method

Numerical or semidiscrete analog approximations to the diffusion equation must be formulated for solutions with automatic computing equipment. The present paper is devoted to the evaluation of truncation errors inherent in the spacewise difference formulation of the equation under general boundary conditions. A general method of analysis is developed and the error between the semidiscrete solution and the exact solution of the partial differential equations is evolved by matrix algebra and the Laplace transform. The method is illustrated by example showing the errors in the case of a symmetrically heated slab subject to temperature boundary conditions expressed as polynomials in time.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

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