{"title":"The numerical solution of the adsorption integral equation with Langmuir-kernel Part 1: approximations","authors":"Steffen Arnrich, Grit Kalies","doi":"10.1007/s10910-025-01724-x","DOIUrl":null,"url":null,"abstract":"<div><p>The qualitative relationship between the adsorption energy distribution of a microporous adsorbent and its total isotherms is modeled by the adsorption integral equation with Langmuir kernel. Due to the instability of the adsorption integral equation, a regularization is required. Recently, we have developed a general regularization using a transformation that will now be specialized for numerical application. In this paper, we perform the first step to this end, namely the construction of an approximation of the transformed total isotherm from finitely many measurement points. The method presented here is based on discrete convolution and is also suitable for the approximation of more general functions and their spectral functions. A full error analysis is given. In particular, the influences of the measurement error, the discretization error and the truncation error on the quality of the approximation of the transformed total isotherm are investigated.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1650 - 1678"},"PeriodicalIF":2.0000,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01724-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-025-01724-x","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
The qualitative relationship between the adsorption energy distribution of a microporous adsorbent and its total isotherms is modeled by the adsorption integral equation with Langmuir kernel. Due to the instability of the adsorption integral equation, a regularization is required. Recently, we have developed a general regularization using a transformation that will now be specialized for numerical application. In this paper, we perform the first step to this end, namely the construction of an approximation of the transformed total isotherm from finitely many measurement points. The method presented here is based on discrete convolution and is also suitable for the approximation of more general functions and their spectral functions. A full error analysis is given. In particular, the influences of the measurement error, the discretization error and the truncation error on the quality of the approximation of the transformed total isotherm are investigated.
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The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
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