Pub Date : 2023-01-27DOI: 10.48550/arXiv.2301.11642
M. Berardi, F. Difonzo, S. F. Pellegrino
Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to peridynamic theory, which allows a proper modeling of non localities in space. In this framework, we make use of Chebyshev transform on the diffusive component of the equation and then we integrate forward in time using an explicit method. We prove that the proposed spectral numerical scheme provides a solution converging to the unique solution in some appropriate Sobolev space. We finally exemplify on several different soils, also considering a sink term representing the root water uptake.
{"title":"A Numerical Method for a Nonlocal Form of Richards' Equation Based on Peridynamic Theory","authors":"M. Berardi, F. Difonzo, S. F. Pellegrino","doi":"10.48550/arXiv.2301.11642","DOIUrl":"https://doi.org/10.48550/arXiv.2301.11642","url":null,"abstract":"Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presence of cracks and fractures can be accomplished resorting to peridynamic theory, which allows a proper modeling of non localities in space. In this framework, we make use of Chebyshev transform on the diffusive component of the equation and then we integrate forward in time using an explicit method. We prove that the proposed spectral numerical scheme provides a solution converging to the unique solution in some appropriate Sobolev space. We finally exemplify on several different soils, also considering a sink term representing the root water uptake.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75445786","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 : 2023-01-12DOI: 10.1007/s40314-023-02185-1
J. Sousa, S. Gala, E. C. Oliveira
{"title":"On the uniqueness of mild solutions to the time-fractional Navier-Stokes equations in $$L^{N} left( mathbb {R} ^{N}right) ^{N}$$","authors":"J. Sousa, S. Gala, E. C. Oliveira","doi":"10.1007/s40314-023-02185-1","DOIUrl":"https://doi.org/10.1007/s40314-023-02185-1","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89522772","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 : 2023-01-10DOI: 10.1007/s40314-022-02160-2
A. Sarkar, N. Deb, A. Biswas
{"title":"Weighted dual hesitant $$q$$-rung orthopair fuzzy sets and their application in multicriteria group decision making based on Hamacher operations","authors":"A. Sarkar, N. Deb, A. Biswas","doi":"10.1007/s40314-022-02160-2","DOIUrl":"https://doi.org/10.1007/s40314-022-02160-2","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82184845","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 : 2023-01-06DOI: 10.1007/s40314-022-02182-w
R. Aslan
{"title":"Approximation properties of univariate and bivariate new class $$lambda $$-Bernstein-Kantorovich operators and its associated GBS operators","authors":"R. Aslan","doi":"10.1007/s40314-022-02182-w","DOIUrl":"https://doi.org/10.1007/s40314-022-02182-w","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86731032","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 : 2023-01-04DOI: 10.48550/arXiv.2301.01670
Pari J. Kundaliya, Sudhakar Chaudhary
In this article, we propose a linearized fully-discrete scheme for solving a time fractional nonlocal diffusion-wave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the $L1$ scheme in time. We derive the $alpha$-robust textit{a priori} bound and textit{a priori} error estimate for the fully-discrete solution in $L^{infty}big(H^1_0(Omega)big)$ norm, where $alpha in (1,2)$ is the order of time fractional derivative. Finally, we perform some numerical experiments to verify the theoretical results.
本文给出了求解时间分数阶Kirchhoff型非局部扩散波方程的线性化全离散格式。该方案在空间上采用有限元法，在时间上采用$L1$方案。我们推导了$L^{infty}big(H^1_0(Omega)big)$范数下全离散解的$alpha$ -鲁棒textit{先验的}界和textit{先验的}误差估计，其中$alpha in (1,2)$为时间阶分数阶导数。最后，通过数值实验对理论结果进行了验证。
{"title":"Symmetric fractional order reduction method with L1 scheme on graded mesh for time fractional nonlocal diffusion-wave equation of Kirchhoff type","authors":"Pari J. Kundaliya, Sudhakar Chaudhary","doi":"10.48550/arXiv.2301.01670","DOIUrl":"https://doi.org/10.48550/arXiv.2301.01670","url":null,"abstract":"In this article, we propose a linearized fully-discrete scheme for solving a time fractional nonlocal diffusion-wave equation of Kirchhoff type. The scheme is established by using the finite element method in space and the $L1$ scheme in time. We derive the $alpha$-robust textit{a priori} bound and textit{a priori} error estimate for the fully-discrete solution in $L^{infty}big(H^1_0(Omega)big)$ norm, where $alpha in (1,2)$ is the order of time fractional derivative. Finally, we perform some numerical experiments to verify the theoretical results.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88830958","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 : 2023-01-01DOI: 10.48550/arXiv.2203.09925
Niklas Angleitner, M. Faustmann, J. Melenk
. In [AFM21a], we proved that the inverse of the stiffness matrix of an h -version finite element method (FEM) applied to scalar second order elliptic boundary value problems can be approximated at an exponential rate in the block rank by H -matrices. Here, we improve on this result in multiple ways: (1) The class of meshes is significantly enlarged and includes certain exponentially graded meshes. (2) The dependence on the polynomial degree p of the discrete ansatz space is made explicit in our analysis. (3) The bound for the approximation error is sharpened, and (4) the proof is simplified.
{"title":"Exponential meshes and H-matrices","authors":"Niklas Angleitner, M. Faustmann, J. Melenk","doi":"10.48550/arXiv.2203.09925","DOIUrl":"https://doi.org/10.48550/arXiv.2203.09925","url":null,"abstract":". In [AFM21a], we proved that the inverse of the stiffness matrix of an h -version finite element method (FEM) applied to scalar second order elliptic boundary value problems can be approximated at an exponential rate in the block rank by H -matrices. Here, we improve on this result in multiple ways: (1) The class of meshes is significantly enlarged and includes certain exponentially graded meshes. (2) The dependence on the polynomial degree p of the discrete ansatz space is made explicit in our analysis. (3) The bound for the approximation error is sharpened, and (4) the proof is simplified.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88162866","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 : 2023-01-01DOI: 10.1007/s40314-023-02257-2
Xiao‐Chuang Jin, Jun‐Guo Lu, Qing‐Hao Zhang
{"title":"Delay-dependent and order-dependent asymptotic stability conditions for Riemann-Liouville fractional-order systems with time delays","authors":"Xiao‐Chuang Jin, Jun‐Guo Lu, Qing‐Hao Zhang","doi":"10.1007/s40314-023-02257-2","DOIUrl":"https://doi.org/10.1007/s40314-023-02257-2","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72775110","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 : 2023-01-01DOI: 10.1007/s40314-022-02149-x
P. Olivares, C. Díaz
{"title":"A finite elements approach for spread contract valuation via associated two-dimensional PIDE","authors":"P. Olivares, C. Díaz","doi":"10.1007/s40314-022-02149-x","DOIUrl":"https://doi.org/10.1007/s40314-022-02149-x","url":null,"abstract":"","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75788164","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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