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

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.

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems

“…Zureigat et al [34] offered two compact finite difference schemes with a fuzzy Caputo generalized Hukuhara derivative to obtain a certain solution for fractional convectiondiffusion equation. Mustafa et al [35,36] solved fractional-order chaotic systems with the Sinc shape function and analyzed drug diffusion via a thin membrane using the differential quadrature approach.…”

Experimental Investigation and Numerical Model for Chloride Diffusivity of Long-Age Fly Ash Cement Slurry

“…Many classical works have been conducted on chloride diffusion characteristics both in experimental aspects and in theoretical aspects [13]. In experiments, based on in situ testing results, Zhang [14] pointed out that the chloride diffusivity showed a slight decrease at a curing age of 28 d with the addition of fly ash into the bulk cement paste.…”