Y. Yaegashi, H. Yoshioka, M. Tsujimura, M. Fujihara
{"title":"Finite volume computation for the non-stationary probability density function of an impulsively controlled 1-D diffusion process","authors":"Y. Yaegashi, H. Yoshioka, M. Tsujimura, M. Fujihara","doi":"10.15748/jasse.7.262","DOIUrl":null,"url":null,"abstract":"We derive a Fokker Planck Equation (FPE) governing probability density functions (PDFs) of an impulsively controlled 1-D diffusion process in seasonal population management problems. Two interventions are considered: perfect (completely controllable) and imperfect interventions (not completely controllable). The FPE is an initialand boundary-value problem subject to a non-local boundary condition along a moving boundary. We show that an finite volume method (FVM) with a domain transformation realizes a conservative discretization for the FPE. We demonstrate that the computed PDFs with the FVM and those with a Monte Carlo method agree well.","PeriodicalId":41942,"journal":{"name":"Journal of Advanced Simulation in Science and Engineering","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Advanced Simulation in Science and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15748/jasse.7.262","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
We derive a Fokker Planck Equation (FPE) governing probability density functions (PDFs) of an impulsively controlled 1-D diffusion process in seasonal population management problems. Two interventions are considered: perfect (completely controllable) and imperfect interventions (not completely controllable). The FPE is an initialand boundary-value problem subject to a non-local boundary condition along a moving boundary. We show that an finite volume method (FVM) with a domain transformation realizes a conservative discretization for the FPE. We demonstrate that the computed PDFs with the FVM and those with a Monte Carlo method agree well.