{"title":"Numerical Solutions of Time Dependent Partial Differential Equations Using Weighted Residual Method With Piecewise Polynomials","authors":"Meraj Alam, Md. Shafiqul Islam","doi":"10.3329/dujs.v67i1.54566","DOIUrl":null,"url":null,"abstract":"We use Galerkin weighted residual (GWR) method to solve one dimensional heat and wave equations as initial and boundary value problems (IBVPs) numerically. Three special types of piecewise polynomials namely: Bernstein, Bernoulli and Legendre polynomials are used as basis functions to solve these IBVPs. A few examples are tested by the proposed method and then the results are compared with the solutions found in other existing methods. The numerical results obtained in this paper are in good agreement with the exact solutions. \nDhaka Univ. J. Sci. 67(1): 5-12, 2019 (January)","PeriodicalId":11280,"journal":{"name":"Dhaka University Journal of Science","volume":"3597 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dhaka University Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/dujs.v67i1.54566","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We use Galerkin weighted residual (GWR) method to solve one dimensional heat and wave equations as initial and boundary value problems (IBVPs) numerically. Three special types of piecewise polynomials namely: Bernstein, Bernoulli and Legendre polynomials are used as basis functions to solve these IBVPs. A few examples are tested by the proposed method and then the results are compared with the solutions found in other existing methods. The numerical results obtained in this paper are in good agreement with the exact solutions.
Dhaka Univ. J. Sci. 67(1): 5-12, 2019 (January)