{"title":"用Aboodh变换求解第二类带凸函数的Volterra积分方程","authors":"Asif Iqbal Ali, Muhammad Kalim, Adnan Khan","doi":"10.32350/sir.62.02","DOIUrl":null,"url":null,"abstract":"A large class of complexities in mathematical physics, applied mathematics, and engineering are expressed as differential equations with few additions and certain conditions. This research article studies the solution of Volterra integral equations of the second kind where bulge functions take as a known function. To obtain an analytical solution, this study uses the Aboodh transform, the Aboodh inverse transform and the convolution theorem whereas it would be required to discover the precise solution of VIEs. We will also compare it with a numerical solution using a modified Simpson method, and finally, we will represent it graphically.","PeriodicalId":137307,"journal":{"name":"Scientific Inquiry and Review","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solution of Volterra integral equations of the 2nd kind with bulge function using Aboodh transform\",\"authors\":\"Asif Iqbal Ali, Muhammad Kalim, Adnan Khan\",\"doi\":\"10.32350/sir.62.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A large class of complexities in mathematical physics, applied mathematics, and engineering are expressed as differential equations with few additions and certain conditions. This research article studies the solution of Volterra integral equations of the second kind where bulge functions take as a known function. To obtain an analytical solution, this study uses the Aboodh transform, the Aboodh inverse transform and the convolution theorem whereas it would be required to discover the precise solution of VIEs. We will also compare it with a numerical solution using a modified Simpson method, and finally, we will represent it graphically.\",\"PeriodicalId\":137307,\"journal\":{\"name\":\"Scientific Inquiry and Review\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scientific Inquiry and Review\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32350/sir.62.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scientific Inquiry and Review","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32350/sir.62.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solution of Volterra integral equations of the 2nd kind with bulge function using Aboodh transform
A large class of complexities in mathematical physics, applied mathematics, and engineering are expressed as differential equations with few additions and certain conditions. This research article studies the solution of Volterra integral equations of the second kind where bulge functions take as a known function. To obtain an analytical solution, this study uses the Aboodh transform, the Aboodh inverse transform and the convolution theorem whereas it would be required to discover the precise solution of VIEs. We will also compare it with a numerical solution using a modified Simpson method, and finally, we will represent it graphically.