Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei
{"title":"求解分数阶种群扩散模型的自适应分层配置方法","authors":"Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei","doi":"10.1155/2023/2323418","DOIUrl":null,"url":null,"abstract":"The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model\",\"authors\":\"Linqiang Yang, Yafei Liu, Hongmei Ma, Xue Liu, Shuli Mei\",\"doi\":\"10.1155/2023/2323418\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.\",\"PeriodicalId\":43667,\"journal\":{\"name\":\"Muenster Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-09-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Muenster Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2023/2323418\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Muenster Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2023/2323418","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Adaptive Hierarchical Collocation Method for Solving Fractional Population Diffusion Model
The fractional population diffusion model is crucial for pest prevention. This paper presents an adaptive hierarchical collocation method for solving this model, enhancing the efficiency of algorithms based on Low-Complexity Shannon-Cosine wavelet derived from combinatorial identity theory. This function, an improvement over previous constructs, mitigates the need for iterative computation of parameters and boasts advantages like interpolation, symmetry, and compact support. The method’s extension to other time-fractional partial differential equations (PDEs) is also possible. The algorithm’s complexity analysis illustrates the concise function’s efficiency advantage over the original expression when solving time-fractional PDEs. Comparatively, the method exhibits superior numerical performance to alternative wavelet spectral methods like the Shannon–Gabor wavelet.