Pub Date : 2022-08-08DOI: 10.1142/s0219876223500196
M. Aparna, P. Paramanathan
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the constructed interpolation functions. Unlike the conventional constructions, each vertex in the partition of the triangular region has been assigned a color such that the chromatic number of the partition is 3. A new method for the partitioning of the triangle is proposed with a result concerning the chromatic number of its graph. Following the construction, a formula determining the vertical scaling factor is provided. With the newly defined vertical scaling factor, it is clearly observed that the value of the double integral coincides with the integral value calculated using fractal theory. Further, a relation connecting the fractal interpolation function with the equation of the plane passing through the vertices of the triangle is established. Convergence of the proposed method to the actual integral value is proven with sufficient lemmas and theorems. Sufficient examples are also provided to illustrate the method of construction and to verify the formula of double integration.
{"title":"Bivariate fractal interpolation functions on triangular domain for numerical integration and approximation","authors":"M. Aparna, P. Paramanathan","doi":"10.1142/s0219876223500196","DOIUrl":"https://doi.org/10.1142/s0219876223500196","url":null,"abstract":"The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the constructed interpolation functions. Unlike the conventional constructions, each vertex in the partition of the triangular region has been assigned a color such that the chromatic number of the partition is 3. A new method for the partitioning of the triangle is proposed with a result concerning the chromatic number of its graph. Following the construction, a formula determining the vertical scaling factor is provided. With the newly defined vertical scaling factor, it is clearly observed that the value of the double integral coincides with the integral value calculated using fractal theory. Further, a relation connecting the fractal interpolation function with the equation of the plane passing through the vertices of the triangle is established. Convergence of the proposed method to the actual integral value is proven with sufficient lemmas and theorems. Sufficient examples are also provided to illustrate the method of construction and to verify the formula of double integration.","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41345920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-21DOI: 10.1142/s0219876221430209
A. Mojahedin, M. Hashemitaheri, M. Salavati, X. Fu, T. Rabczuk
{"title":"A deep energy method for the analysis of thermoporoelastic functionally-graded beams","authors":"A. Mojahedin, M. Hashemitaheri, M. Salavati, X. Fu, T. Rabczuk","doi":"10.1142/s0219876221430209","DOIUrl":"https://doi.org/10.1142/s0219876221430209","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41729914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-21DOI: 10.1142/s0219876222500347
Abderahim Belounar, L. Belounar, A. Tati
{"title":"An assumed strain finite element for composite plates analysis","authors":"Abderahim Belounar, L. Belounar, A. Tati","doi":"10.1142/s0219876222500347","DOIUrl":"https://doi.org/10.1142/s0219876222500347","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43192456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-21DOI: 10.1142/s0219876222500323
Amit Sharma, Pratima Rai
{"title":"Analysis of a hybrid numerical scheme for singularly perturbed convection-diffusion type delay problems","authors":"Amit Sharma, Pratima Rai","doi":"10.1142/s0219876222500323","DOIUrl":"https://doi.org/10.1142/s0219876222500323","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42415852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：