{"title":"Fractal Multiquadric Interpolation Functions","authors":"D. Kumar, A. K. B. Chand, P. R. Massopust","doi":"10.1137/23m1578917","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2349-2369, October 2024. <br/> Abstract. In this article, we impose fractal features onto classical multiquadric (MQ) functions. This generates a novel class of fractal functions, called fractal MQ functions, where the symmetry of the original MQ function with respect to the origin is maintained. This construction requires a suitable extension of the domain and similar partitions on the left side with the same choice of scaling parameters. Smooth fractal MQ functions are proposed to solve initial value problems via a collocation method. Our numerical computations suggest that fractal MQ functions offer higher accuracy and more flexibility for the solutions compared to the existing classical MQ functions. Some approximation results associated with fractal MQ functions are also presented.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"80 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1578917","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2349-2369, October 2024. Abstract. In this article, we impose fractal features onto classical multiquadric (MQ) functions. This generates a novel class of fractal functions, called fractal MQ functions, where the symmetry of the original MQ function with respect to the origin is maintained. This construction requires a suitable extension of the domain and similar partitions on the left side with the same choice of scaling parameters. Smooth fractal MQ functions are proposed to solve initial value problems via a collocation method. Our numerical computations suggest that fractal MQ functions offer higher accuracy and more flexibility for the solutions compared to the existing classical MQ functions. Some approximation results associated with fractal MQ functions are also presented.
期刊介绍：
SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.
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