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

Author

Listed:
  • Abdelfattah Mustafa

    (Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia)

  • Reda S. Salama

    (Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt)

  • Mokhtar Mohamed

    (Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt)

Abstract

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.

Suggested Citation

  • Abdelfattah Mustafa & Reda S. Salama & Mokhtar Mohamed, 2023. "Semi-Analytical Analysis of Drug Diffusion through a Thin Membrane Using the Differential Quadrature Method," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2998-:d:1187407
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    References listed on IDEAS

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    1. Ola Ragb & Mokhtar Mohamed & M.S. Matbuly, 2019. "Vibration Analysis of Magneto-Electro-Thermo NanoBeam Resting on Nonlinear Elastic Foundation Using Sinc and Discrete Singular Convolution Differential Quadrature Method," Modern Applied Science, Canadian Center of Science and Education, vol. 13(7), pages 1-49, July.
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    Cited by:

    1. Jian Chen & Feng-Yan Qi & Meng-Yan Jia & Wen-Bing Song & Jian Zhang & Jian-Jun Zheng, 2023. "Experimental Investigation and Numerical Model for Chloride Diffusivity of Long-Age Fly Ash Cement Slurry," Sustainability, MDPI, vol. 15(20), pages 1-20, October.

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