{"title":"求解Bratu方程的基于Bernoulli多项式和移位Chebychev的配置方法","authors":"M. El-Gamel, W. Adel, M. El-Azab","doi":"10.4172/2168-9679.1000407","DOIUrl":null,"url":null,"abstract":"In this work, Bernoulli-collocation method is proposed for solving nonlinear Bratu's type equations. The operational matrix of derivative of Bernoulli is introduced. The matrix together with the collocation method are then utilized to reduce the problem into a system of nonlinear algebraic equations. Also, a reliable approach for solving this nonlinear system is discussed. Numerical results and comparisons with other existing methods provided in the literature are made. Citation: EL-Gamel M, Adel W, EL-Azab MS (2018) Collocation Method Based on Bernoulli Polynomial and Shifted Chebychev for Solving the Bratu Equation. J Appl Computat Math 7: 407. doi: 10.4172/2168-9679.1000407","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"48 2 1","pages":"1-7"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Collocation Method Based on Bernoulli Polynomial and Shifted Chebychev for Solving the Bratu Equation\",\"authors\":\"M. El-Gamel, W. Adel, M. El-Azab\",\"doi\":\"10.4172/2168-9679.1000407\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, Bernoulli-collocation method is proposed for solving nonlinear Bratu's type equations. The operational matrix of derivative of Bernoulli is introduced. The matrix together with the collocation method are then utilized to reduce the problem into a system of nonlinear algebraic equations. Also, a reliable approach for solving this nonlinear system is discussed. Numerical results and comparisons with other existing methods provided in the literature are made. Citation: EL-Gamel M, Adel W, EL-Azab MS (2018) Collocation Method Based on Bernoulli Polynomial and Shifted Chebychev for Solving the Bratu Equation. J Appl Computat Math 7: 407. doi: 10.4172/2168-9679.1000407\",\"PeriodicalId\":15007,\"journal\":{\"name\":\"Journal of Applied and Computational Mathematics\",\"volume\":\"48 2 1\",\"pages\":\"1-7\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Computational Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4172/2168-9679.1000407\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4172/2168-9679.1000407","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Collocation Method Based on Bernoulli Polynomial and Shifted Chebychev for Solving the Bratu Equation
In this work, Bernoulli-collocation method is proposed for solving nonlinear Bratu's type equations. The operational matrix of derivative of Bernoulli is introduced. The matrix together with the collocation method are then utilized to reduce the problem into a system of nonlinear algebraic equations. Also, a reliable approach for solving this nonlinear system is discussed. Numerical results and comparisons with other existing methods provided in the literature are made. Citation: EL-Gamel M, Adel W, EL-Azab MS (2018) Collocation Method Based on Bernoulli Polynomial and Shifted Chebychev for Solving the Bratu Equation. J Appl Computat Math 7: 407. doi: 10.4172/2168-9679.1000407
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