Drug release from polymeric platforms for non smooth solutions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI:10.1016/j.apnum.2025.02.016

J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi

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引用次数: 0

Abstract

This paper aims to conclude a sequence of works focused in the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were

C^{4}

- functions. In the present work, our aim is to establish second order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are

H^{3}

- functions. Numerical experiments illustrating the obtained theoretical results are also included.

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非光滑溶液的聚合物平台药物释放

本文的目的是总结一系列工作集中在非均匀网格中的偏微分方程组的数值研究，该系统可用于描述药物从聚合物平台的释放。药物释放是非菲克流体摄取、溶解过程和菲克药物运输的结果。计算工具的发展及其理论支持是共同的驱动力。在作者之前的工作中，考虑溶液的严重平滑假设：溶剂和溶解药物都是C4-函数，对溶剂、固体药物和溶解药物的数值近似建立了二阶误差估计。在目前的工作中，我们的目标是为相同的变量建立二阶估计，减少平滑假设，即我们假设溶剂和溶解的药物是H3-函数。文中还进行了数值实验，对所得理论结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.