Pub Date : 2022-11-24DOI: 10.1186/s13662-022-03737-1
Shahnaz Karami, A. Fakharzadeh Jahromi, M. Heydari
{"title":"A computational method based on the generalized Lucas polynomials for fractional optimal control problems","authors":"Shahnaz Karami, A. Fakharzadeh Jahromi, M. Heydari","doi":"10.1186/s13662-022-03737-1","DOIUrl":"https://doi.org/10.1186/s13662-022-03737-1","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43395264","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 : 2022-10-21DOI: 10.1186/s13662-022-03730-8
Juncheng Li, Chengzhi Liu, Shanjun Liu
{"title":"The quartic Catmull–Rom spline with local adjustability and its shape optimization","authors":"Juncheng Li, Chengzhi Liu, Shanjun Liu","doi":"10.1186/s13662-022-03730-8","DOIUrl":"https://doi.org/10.1186/s13662-022-03730-8","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777401","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 : 2022-10-01DOI: 10.1186/s13662-022-03729-1
Tianfu Ji, Jianhua Hou, Changqing Yang
{"title":"The operational matrix of Chebyshev polynomials for solving pantograph-type Volterra integro-differential equations","authors":"Tianfu Ji, Jianhua Hou, Changqing Yang","doi":"10.1186/s13662-022-03729-1","DOIUrl":"https://doi.org/10.1186/s13662-022-03729-1","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44113890","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 : 2022-09-06DOI: 10.48550/arXiv.2209.02689
L. Lopez, S. F. Pellegrino
Peridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As a consequence, it finds applications in the framework of the development and evolution of fractures and damages in elastic materials. In this paper we consider a one-dimensional nonlinear model of peridynamics and propose a suitable two-dimensional fast-convolution spectral method based on Chebyshev polynomials to solve the model. This choice allows us to gain the same accuracy both in space and time. We show the convergence of the method and perform several simulations to study the performance of the spectral scheme.
{"title":"A fast-convolution based space–time Chebyshev spectral method for peridynamic models","authors":"L. Lopez, S. F. Pellegrino","doi":"10.48550/arXiv.2209.02689","DOIUrl":"https://doi.org/10.48550/arXiv.2209.02689","url":null,"abstract":"Peridynamics is a nonlocal generalization of continuum mechanics theory which addresses discontinuous problems without using partial derivatives and replacing them by an integral operator. As a consequence, it finds applications in the framework of the development and evolution of fractures and damages in elastic materials. In this paper we consider a one-dimensional nonlinear model of peridynamics and propose a suitable two-dimensional fast-convolution spectral method based on Chebyshev polynomials to solve the model. This choice allows us to gain the same accuracy both in space and time. We show the convergence of the method and perform several simulations to study the performance of the spectral scheme.","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48350493","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 : 2022-09-01DOI: 10.1186/s13662-022-03728-2
Jalil Mazloum, B. Hadian Siahkal-Mahalle
{"title":"A time-splitting local meshfree approach for time-fractional anisotropic diffusion equation: application in image denoising","authors":"Jalil Mazloum, B. Hadian Siahkal-Mahalle","doi":"10.1186/s13662-022-03728-2","DOIUrl":"https://doi.org/10.1186/s13662-022-03728-2","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777359","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 : 2022-09-01DOI: 10.1186/s13662-022-03727-3
M. Huntul, M. Abbas
{"title":"An inverse problem of fourth-order partial differential equation with nonlocal integral condition","authors":"M. Huntul, M. Abbas","doi":"10.1186/s13662-022-03727-3","DOIUrl":"https://doi.org/10.1186/s13662-022-03727-3","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65777730","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 : 2022-07-13DOI: 10.1186/s13662-022-03732-6
Nunzio Dimola, A. Coclite, G. Fanizza, T. Politi
{"title":"Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics","authors":"Nunzio Dimola, A. Coclite, G. Fanizza, T. Politi","doi":"10.1186/s13662-022-03732-6","DOIUrl":"https://doi.org/10.1186/s13662-022-03732-6","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46161165","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 : 2022-07-02DOI: 10.1186/s13662-023-03761-9
D. Ruelle
{"title":"The nature of properly human mathematics","authors":"D. Ruelle","doi":"10.1186/s13662-023-03761-9","DOIUrl":"https://doi.org/10.1186/s13662-023-03761-9","url":null,"abstract":"","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48874629","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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