Pub Date : 2016-01-22DOI: 10.6084/M9.FIGSHARE.3113629.V1
Mohsen Soori, S. Nourazar, A. Nazari-Golshan
To obtain the exact solution of the Fisher Type equation, the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM) are used. Obtained results by using the methods are numerically compared to present accuracy of the algorithms in solving the equation. The results prove that the methods are effective and powerful algorithm in order to solve the Fisher type equation as a non-linear differential equation.
{"title":"Application of the Variational Iteration Method and the Homotopy Perturbation Method to the Fisher Type Equation","authors":"Mohsen Soori, S. Nourazar, A. Nazari-Golshan","doi":"10.6084/M9.FIGSHARE.3113629.V1","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.3113629.V1","url":null,"abstract":"To obtain the exact solution of the Fisher Type equation, the Variational Iteration Method (VIM) and the Homotopy Perturbation Method (HPM) are used. Obtained results by using the methods are numerically compared to present accuracy of the algorithms in solving the equation. The results prove that the methods are effective and powerful algorithm in order to solve the Fisher type equation as a non-linear differential equation.","PeriodicalId":202423,"journal":{"name":"International Journal of Mathematics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122504388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the Homotopy Perturbation Method (HPM) is used to solve the Fitzhugh–Nagumo non-linear differential equations. In order to obtain the exact solution of Fitzhugh–Nagumo equation, two case study problems of the equation are solved by using the HPM. The trend of the rapid convergence of the sequences constructed by the method towards the exact solution is also numerically shown. As a result, the rapid convergence towards the exact solutions of HPM indicates that the method is powerful and efficient technique to solve the Fitzhugh–Nagumo non-linear differential equations. Also, the results present validity and great potential of the method as a powerful algorithm in order to obtain the exact solution of nonlinear differential equations.
{"title":"On the Homotopy Perturbation Method for the Exact Solution of Fitzhugh–Nagumo Equation","authors":"S. Nourazar, Mohsen Soori, Akbar Nazar-Golshan","doi":"10.5281/ZENODO.47783","DOIUrl":"https://doi.org/10.5281/ZENODO.47783","url":null,"abstract":"In this paper, the Homotopy Perturbation Method (HPM) is used to solve the Fitzhugh–Nagumo non-linear differential equations. In order to obtain the exact solution of Fitzhugh–Nagumo equation, two case study problems of the equation are solved by using the HPM. The trend of the rapid convergence of the sequences constructed by the method towards the exact solution is also numerically shown. As a result, the rapid convergence towards the exact solutions of HPM indicates that the method is powerful and efficient technique to solve the Fitzhugh–Nagumo non-linear differential equations. Also, the results present validity and great potential of the method as a powerful algorithm in order to obtain the exact solution of nonlinear differential equations.","PeriodicalId":202423,"journal":{"name":"International Journal of Mathematics and Computation","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122128491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2009-03-20DOI: 10.12732/IJDEA.V14I4.2456
S. A. Iyase, P. O. Aiyelo
We prove the existence of periodic solutions for equation (1.1) using degree theoretic methods. The uniqueness of periodic solutions is also examined.
利用次理论方法证明了方程(1.1)周期解的存在性。本文还研究了周期解的唯一性。
{"title":"Resonant Oscillation Of Certain Fourth Order Nonlinear Differential Equations With Delay","authors":"S. A. Iyase, P. O. Aiyelo","doi":"10.12732/IJDEA.V14I4.2456","DOIUrl":"https://doi.org/10.12732/IJDEA.V14I4.2456","url":null,"abstract":"We prove the existence of periodic solutions for equation (1.1) using degree theoretic methods. The uniqueness of periodic solutions is also examined.","PeriodicalId":202423,"journal":{"name":"International Journal of Mathematics and Computation","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127653356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.1007/978-3-319-24747-2_1
M. Bohner, Sabrina H. Streipert
{"title":"The Beverton–Holt q-Difference Equation with Periodic Growth Rate","authors":"M. Bohner, Sabrina H. Streipert","doi":"10.1007/978-3-319-24747-2_1","DOIUrl":"https://doi.org/10.1007/978-3-319-24747-2_1","url":null,"abstract":"","PeriodicalId":202423,"journal":{"name":"International Journal of Mathematics and Computation","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130122561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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