Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method
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...
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| Format: | Article |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2998 |
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| author | Abdelfattah Mustafa Reda S. Salama Mokhtar Mohamed |
| author_facet | Abdelfattah Mustafa Reda S. Salama Mokhtar Mohamed |
| author_sort | Abdelfattah Mustafa |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T01:34:08Z |
| format | Article |
| id | doaj.art-5c50167ab1134345aa4508016993b18c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:34:08Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5c50167ab1134345aa4508016993b18c2023-11-18T17:04:21ZengMDPI AGMathematics2227-73902023-07-011113299810.3390/math11132998Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature MethodAbdelfattah Mustafa0Reda S. Salama1Mokhtar Mohamed2Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi ArabiaBasic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, EgyptBasic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, EgyptThe 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.https://www.mdpi.com/2227-7390/11/13/2998group theoretic methoddrug diffusiondifferential quadrature techniquediscrete singular convolutionthin membraneLagrange interpolation polynomial |
| spellingShingle | Abdelfattah Mustafa Reda S. Salama Mokhtar Mohamed Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method Mathematics group theoretic method drug diffusion differential quadrature technique discrete singular convolution thin membrane Lagrange interpolation polynomial |
| title | Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method |
| title_full | Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method |
| title_fullStr | Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method |
| title_full_unstemmed | Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method |
| title_short | Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method |
| title_sort | semi analytical analysis of drug diffusion through a thin membrane using the differential quadrature method |
| topic | group theoretic method drug diffusion differential quadrature technique discrete singular convolution thin membrane Lagrange interpolation polynomial |
| url | https://www.mdpi.com/2227-7390/11/13/2998 |
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