{"title":"Bezier多项式及其应用","authors":"Nazrul Islam, M. Islam","doi":"10.3329/dujs.v66i2.54562","DOIUrl":null,"url":null,"abstract":"In this paper, we use the Galerkin technique for solving higher order linear and nonlinear boundary value problems (BVPs). The well-known Bezier polynomials are exploited as basis functions in the technique. To use the Bezier polynomials, we need to satisfy the corresponding homogeneous form of the boundary conditions and modification is thus needed. A rigorous matrix formulation is developed by the Galerkin method for linear and nonlinear systems and solved it using Bezier polynomials. The approximate solutions are compared to the exact solutions through tabular form. All problems are computed using the software MATHEMATICA. \nDhaka Univ. J. Sci. 66(2): 157-162, 2018 (July)","PeriodicalId":11280,"journal":{"name":"Dhaka University Journal of Science","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bezier Polynomials with Applications\",\"authors\":\"Nazrul Islam, M. Islam\",\"doi\":\"10.3329/dujs.v66i2.54562\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we use the Galerkin technique for solving higher order linear and nonlinear boundary value problems (BVPs). The well-known Bezier polynomials are exploited as basis functions in the technique. To use the Bezier polynomials, we need to satisfy the corresponding homogeneous form of the boundary conditions and modification is thus needed. A rigorous matrix formulation is developed by the Galerkin method for linear and nonlinear systems and solved it using Bezier polynomials. The approximate solutions are compared to the exact solutions through tabular form. All problems are computed using the software MATHEMATICA. \\nDhaka Univ. J. Sci. 66(2): 157-162, 2018 (July)\",\"PeriodicalId\":11280,\"journal\":{\"name\":\"Dhaka University Journal of Science\",\"volume\":\"63 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dhaka University Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/dujs.v66i2.54562\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dhaka University Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/dujs.v66i2.54562","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we use the Galerkin technique for solving higher order linear and nonlinear boundary value problems (BVPs). The well-known Bezier polynomials are exploited as basis functions in the technique. To use the Bezier polynomials, we need to satisfy the corresponding homogeneous form of the boundary conditions and modification is thus needed. A rigorous matrix formulation is developed by the Galerkin method for linear and nonlinear systems and solved it using Bezier polynomials. The approximate solutions are compared to the exact solutions through tabular form. All problems are computed using the software MATHEMATICA.
Dhaka Univ. J. Sci. 66(2): 157-162, 2018 (July)
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