scholarly journals THE METHOD OF LINES FOR SOLUTION OF ONE-DIMENSIONAL DIFFUSION-REACTION EQUATION DESCRIBING CONCENTRATION OF DISSOLVED OXYGEN IN A POLLUTED RIVER

2021 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Dissolved Oxygen ◽  
Method Of Lines ◽  
Diffusion Reaction ◽  
Reaction Equation ◽  
Polluted River ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
The Method Of Lines

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hamid Mesgarani ◽  
Mahya Kermani ◽  
Mostafa Abbaszadeh
Keyword(s):  
Method Of Lines ◽  
Variable Coefficients ◽  
Diffusion Reaction ◽  
Test Problems ◽  
Reaction Equation ◽  
Content Type ◽  
Interpolation Matrix ◽  
Advection Diffusion ◽  
The Method Of Lines ◽  
Nonlinear Advection

Purpose The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients. Design/methodology/approach The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well. Findings Several test problems are provided to confirm the validity and efficiently of the proposed method. Originality/value For the first time, some famous examples are solved by using the proposed high-order technique.

scholarly journals Method of lines for solving linear equations of mathematical physics with the third and first types boundary conditions

2021 ◽  
Vol 2131 (3) ◽  
pp. 032041
Author(s):  
M Kh Eshmurodov ◽  
K M Shaimov ◽  
I Khujaev ◽  
J Khujaev
Keyword(s):  
Boundary Conditions ◽  
Characteristic Equation ◽  
Transition Matrix ◽  
Method Of Lines ◽  
Mathematical Physics ◽  
Sweep Method ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
The Third ◽  
The Method Of Lines

Abstract The use of the method of lines in solving multidimensional problems of mathematical physics makes it possible to eliminate the discrepancies caused by the use of the sweep method in certain coordinates. As a result, the solution of the Poisson equation, for example, is obtained without using the relaxation method. In the article, the problem on the eigenvalues and vectors of the transition matrix is solved for boundary conditions of the third and first types, used to solve a one-dimensional equation of parabolic type by the method of lines. Due to the features of boundary conditions of the third type for determining the eigenvalues, a mixed method was proposed based on the Vieta theorem and the representation of the characteristic equation in trigonometric form typical for the method of lines. To solve the eigenvector problem, a simple sweep method was used with the algebraic compliments to the transition matrix. Discontinuous solutions of a one-dimensional parabolic equation were presented for various values of complex 1 -αl; the method for solving the characteristic equation was selected based on these values. The calculation results are in good agreement with the analytical solution.

Modeling of Membrane Reactor

2002 ◽  
Vol 1 (1) ◽  
Author(s):  
Karl A. Hoff ◽  
Jana Poplsteinova ◽  
Hugo A. Jakobsen ◽  
Olav Falk-Pedersen ◽  
Olav Juliussen ◽  
...  
Keyword(s):  
Membrane Reactor ◽  
Fluid Dynamic ◽  
Method Of Lines ◽  
Diffusion Reaction ◽  
Experimental Unit ◽  
Membrane Pore ◽  
Diffusion Parameters ◽  
The Method Of Lines ◽  
Volume Method ◽  
Experimental Absorption

A two-dimensional model for a membrane reactor used for the absorption of CO2 into amines was developed and two solution procedures were tested for the combined diffusion-reaction problem. The method of lines/finite difference method is the fastest and most stable, but conservation of mass is not guaranteed. The finite volume method needs very good initial estimates to converge, and is much slower. This shows a potential problem in the use of commercial CFD-codes for coupled fluid dynamic, diffusion, and chemical reaction problems. The model has been validated with respect to effects of steep wall diffusivity profiles, membrane pore penetration, and available gas/liquid contact area. The agreement between simulated and experimental absorption fluxes is very good, and the experimental unit is found to have good sensitivity for obtaining kinetic and diffusion parameters.

scholarly journals Asymptotic Solution for a Water Quality Model in a Uniform Stream

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Fazle Mabood ◽  
Nopparat Pochai
Keyword(s):  
Mathematical Modeling ◽  
Water Quality ◽  
Diffusion Reaction ◽  
Order Method ◽  
Quality Model ◽  
Reaction Equation ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Optimal Homotopy Asymptotic Method ◽  
Uniform Stream

We employ approximate analytical method, namely, Optimal Homotopy Asymptotic Method (OHAM), to investigate a one-dimensional steady advection-diffusion-reaction equation with variable inputs arises in the mathematical modeling of dispersion of pollutants in water is proposed. Numerical values are obtained via Runge-Kutta-Fehlberg fourth-fifth order method for comparison purpose. It was found that OHAM solution agrees well with the numerical solution. An example is included to demonstrate the efficiency, accuracy, and simplicity of the proposed method.

scholarly journals An efficient numerical method for one-dimensional hyperbolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01002
Author(s):  
Chartese Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Method Of Lines ◽  
Interface Problems ◽  
Uniform Mesh ◽  
One Dimensional ◽  
Immersed Finite Element ◽  
New Methods ◽  
The Method Of Lines

In this paper, we develop an efficient numerical scheme for solving one-dimensional hyperbolic interface problems. The immersed finite element (IFE) method is used for spatial discretization, which allows the solution mesh to be independent of the interface. Consequently, a fixed uniform mesh can be used throughout the entire simulation. The method of lines is used for temporal discretization. Numerical experiments are provided to show the features of these new methods.

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