A method of solution for a non-linear diffusion model and for computing the parameters in the model

Spoelstra, John; Wyk, D.J. van

doi:10.1016/0377-0427(87)90156-7

Cited by 5 publications

(4 citation statements)

References 2 publications

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“…Non-linear partial differential equation, has been solved using Lie group analysis, and C(x, t) and P(x, t) have been evaluated analytically using the parameters of an experimental Study [8]. The results obtained map the state of the membrane in a way similar to the one obtained by Spoelstra and van Wyk [8], using a finite-difference method.…”

Section: Discussionmentioning

confidence: 99%

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Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Mb¹,

Am²

2015

J Generalized Lie Theory Appl

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The Lie group method is applied to study the diffusion process of drugs across a biological membrane which tends to partially absorb the drug. For the diffusion coefficient, we considered two cases. The Lie group analysis is based on reducing the number of independent variables by one, and consequently the mathematical model described by nonlinear partial differential equation to, covers the diffusion process with the boundary and initial conditions, and is transformed into an ordinary differential equation with the corresponding conditions. The obtained nonlinear ordinary differential equation is solved numerically using the 4 th and 5 th Runge Kutta method, and the results are illustrated graphically and in tables too.

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Section: Discussionmentioning

confidence: 99%

“…Spoelstra and Van Wyk [8] described the process as it is modeled by two cells of the same volume, called donor and the receiver cells, which are separated by a thin membrane. In the donor cell a high concentration of a drug in a saline solution is placed and the receiver cell contains only a saline solution.…”

Section: Introductionmentioning

confidence: 99%

Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Mb¹,

Am²

2015

J Generalized Lie Theory Appl

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“…Fick's-law-based diffusion mathematical models do not apply to human skin, hair-free rodent skin membranes, or multiple synthetic membranes [5]. Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…This method was used to determine the drug concentration in the membrane and that in the cells of the donor and receiver [4]. Spoelstra and Van Wyk [5] modeled the process as a pair of cells of identical volume divided by a thin membrane called cells of the donor and the receiver. A high drug concentration dissolves in a saltwater solution in the cell of a donor, while the receiver's cell possesses only a solution of saline.…”

Section: Introductionmentioning

confidence: 99%

Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method

2023

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The primary goal of this work is to solve the problem of drug diffusion through a thin membrane using a differential quadrature approach with drastically different shape functions, such as Lagrange interpolation and discrete singular convolution (the delta Lagrange kernel and the regularized Shannon kernel). A nonlinear partial differential equation with two time- and space-dependent variables governs the system. To reduce the two independent variables by one, the partial differential equation is transformed into an ordinary differential equation using a one-parameter group transformation. With the aid of the iterative technique, the differential quadrature methods change this equation into an algebraic equation. Then, using a MATLAB program, a code is created that solves this equation for each shape function. To ensure the validity, efficiency, and accuracy of the developed techniques, the computed results are compared to previous numerical and analytical solutions. In addition, the L∞ error is applied. As a consequence of the numerical outcomes, the differential quadrature method, which is primarily based on a discrete singular convolution shape function, is an effective numerical method that can be used to solve the problem of drug diffusion through a thin membrane, guaranteeing a higher accuracy, faster convergence, and greater reliability than other techniques.

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The modelling of oil agglomeration of coal fines

Spoelstra

1989

Journal of Computational and Applied Mathematics

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A method of solution for a non-linear diffusion model and for computing the parameters in the model

Cited by 5 publications

References 2 publications

Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Lie Group Analysis for Solving the Problem of Diffusion of Drugs across a Biological Membrane

Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method

The modelling of oil agglomeration of coal fines

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