{"title":"基于Heronian均值的正交算法解常微分方程初值问题","authors":"Bazuaye Frank Etin-Osa","doi":"10.11648/J.IJAMTP.20190502.12","DOIUrl":null,"url":null,"abstract":"Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution of an Initial Value Problemin Ordinary Differential Equations Using the Quadrature Algorithm Based on the Heronian Mean\",\"authors\":\"Bazuaye Frank Etin-Osa\",\"doi\":\"10.11648/J.IJAMTP.20190502.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.\",\"PeriodicalId\":367229,\"journal\":{\"name\":\"International Journal of Applied Mathematics and Theoretical Physics\",\"volume\":\"53 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Mathematics and Theoretical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11648/J.IJAMTP.20190502.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mathematics and Theoretical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/J.IJAMTP.20190502.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solution of an Initial Value Problemin Ordinary Differential Equations Using the Quadrature Algorithm Based on the Heronian Mean
Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.