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Conservative second-order finite difference method for Camassa–Holm equation with periodic boundary condition 具有周期边界条件的Camassa-Holm方程的保守二阶有限差分法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-09-08 DOI: 10.1080/00207160.2023.2254413
Yufeng Xu, Pintao Zhao, Zhijian Ye, Zhoushun Zheng
{"title":"Conservative second-order finite difference method for Camassa–Holm equation with periodic boundary condition","authors":"Yufeng Xu, Pintao Zhao, Zhijian Ye, Zhoushun Zheng","doi":"10.1080/00207160.2023.2254413","DOIUrl":"https://doi.org/10.1080/00207160.2023.2254413","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90502472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model 缓变时间分数阶Black-Scholes模型的非等时间步长快速紧凑差分格式
4区 数学
International Journal of Computer Mathematics Pub Date : 2023-09-06 DOI: 10.1080/00207160.2023.2254412
Jinfeng Zhou, Xian-Ming Gu, Yong-Liang Zhao, Hu Li
{"title":"A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black-Scholes model","authors":"Jinfeng Zhou, Xian-Ming Gu, Yong-Liang Zhao, Hu Li","doi":"10.1080/00207160.2023.2254412","DOIUrl":"https://doi.org/10.1080/00207160.2023.2254412","url":null,"abstract":"The Black-Scholes (B-S) equation has been recently extended as a kind of tempered time-fractional B-S equations, which becomes an interesting mathematical model in option pricing. In this study, we provide a fast numerical method to approximate the solution of the tempered time-fractional B-S model. To achieve high-order accuracy in space and overcome the weak initial singularity of exact solution, we combine the compact difference operator with L1-type approximation under nonuniform time steps to yield the numerical scheme. The convergence of the proposed difference scheme is proved to be unconditionally stable. Moreover, the kernel function in the tempered Caputo fractional derivative is approximated by sum-of-exponentials, which leads to a fast unconditionally stable compact difference method that reduces the computational cost. Finally, numerical results demonstrate the effectiveness of the proposed methods.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135098101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Mathematical modelling of frailty, dependency and mortality in a 70-year-old general population. 70岁普通人群虚弱、依赖和死亡率的数学模型。
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-08-16 DOI: 10.1080/00207160.2023.2248303
S. Camacho Torregrosa, C. Santamaría Navarro, X. Albert Ros
{"title":"Mathematical modelling of frailty, dependency and mortality in a 70-year-old general population.","authors":"S. Camacho Torregrosa, C. Santamaría Navarro, X. Albert Ros","doi":"10.1080/00207160.2023.2248303","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248303","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73796739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The virtual element method for solving two-dimensional fractional cable equation on general polygonal meshes 一般多边形网格上二维分数阶索方程的虚元法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-08-15 DOI: 10.1080/00207160.2023.2248288
Jixiao Guo, Yanping Chen, Jianwei Zhou, Yuanfei Huang
{"title":"The virtual element method for solving two-dimensional fractional cable equation on general polygonal meshes","authors":"Jixiao Guo, Yanping Chen, Jianwei Zhou, Yuanfei Huang","doi":"10.1080/00207160.2023.2248288","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248288","url":null,"abstract":"In this paper, the conforming virtual element method (VEM) is considered to solve the two-dimensional fractional cable equation involving two Riemann–Liouville fractional derivatives. We adopt the Backward Euler Method and the classical scheme for the numerical discrete scheme of the time derivative. Meanwhile, the conforming VEM, which is generated for arbitrary order of accuracy and the arbitrary polygonal meshes, is analysed for the discretization of the spatial direction. Based on the energy projection operator, the fully discrete formula is proved to be unconditionally stable, and the optimal convergence results are derived with regard to the -norm in detail. Finally, some numerical experiments are implemented to verify the theoretical results.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80139567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel second-order nonstandard finite difference method preserving dynamical properties of a general single-species model 一种新颖的二阶非标准有限差分法，保留了一般单种模型的动力学性质
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-08-15 DOI: 10.1080/00207160.2023.2248304
M. T. Hoang
{"title":"A novel second-order nonstandard finite difference method preserving dynamical properties of a general single-species model","authors":"M. T. Hoang","doi":"10.1080/00207160.2023.2248304","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248304","url":null,"abstract":"In this paper, we extend the Mickens' methodology to construct a second-order nonstandard finite difference (NSFD) method, which preserves dynamical properties including positivity, local asymptotic stability and especially, global asymptotic stability of a general single-species model. This NSFD method is based on a novel weighted non-local approximation of the right-hand side function in combination with the renormalization of the denominator function. The weight guarantees the dynamic consistency and the nonstandard denominator function ensures the convergence of order 2 of the NSFD method. The result is that we obtain a second-order and dynamically consistent NSFD method. It is proved that the NSFD method is simple and efficient and can be extended for solving a broad range of mathematical models arising in real-world applications. Also, we combine the constructed second-order NSFD method with Richardson's extrapolation technique to generate high-order numerical approximations. Finally, the theoretical findings are illustrated and supported by numerical experiments.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83465421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A novel radial basis procedure for the SIRC epidemic delay differential model 一种新的径向基方法求解SIRC流行病延迟微分模型
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-08-15 DOI: 10.1080/00207160.2023.2248286
Z. Sabir, D. Baleanu, F. Mallawi, M. Z. Ullah
{"title":"A novel radial basis procedure for the SIRC epidemic delay differential model","authors":"Z. Sabir, D. Baleanu, F. Mallawi, M. Z. Ullah","doi":"10.1080/00207160.2023.2248286","DOIUrl":"https://doi.org/10.1080/00207160.2023.2248286","url":null,"abstract":"The purpose of this work is to construct a reliable stochastic framework for solving the SIRC delay differential epidemic system, i.e. SIRC-DDES that is based on the coronavirus dynamics. The design of radial basis (RB) transfer function with the optimization of Bayesian regularization neural network (RB-BRNN) is presented to solve the SIRC-DDES. The SIRC-DDES is classified into susceptible , infected , recovered and cross-immune . The exactness of the RB-BRNN is performed for three cases of SIRC-DDES by using the performances of the obtained and reference results. The mean square error is reduced by using the training, testing and substantiation performances with the reference solutions. The small values of the absolute error around 10−07 to 10−08 and different statistical operator performances based on the error histogram values, transitions of state investigations, correlation and regression tests also approve the accuracy of the proposed technique.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75143180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computationally efficient techniques for spatial regression with differential regularization 具有微分正则化的空间回归计算效率技术
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-08-03 DOI: 10.1080/00207160.2023.2239944
Eleonora Arnone, C. de Falco, L. Formaggia, Giorgio Meretti, L. Sangalli
{"title":"Computationally efficient techniques for spatial regression with differential regularization","authors":"Eleonora Arnone, C. de Falco, L. Formaggia, Giorgio Meretti, L. Sangalli","doi":"10.1080/00207160.2023.2239944","DOIUrl":"https://doi.org/10.1080/00207160.2023.2239944","url":null,"abstract":"We investigate some computational aspects of an innovative class of PDE-regularized statistical models: Spatial Regression with Partial Differential Equation regularization (SR-PDE). These physics-informed regression methods can account for the physics of the underlying phenomena and handle data observed over spatial domains with nontrivial shapes, such as domains with concavities and holes or curved domains. The computational bottleneck in SR-PDE estimation is the solution of a computationally demanding linear system involving a low-rank but dense block. We address this aspect by innovatively using Sherman–Morrison–Woodbury identity. We also investigate the efficient selection of the smoothing parameter in SR-PDE estimates. Specifically, we propose ad hoc optimization methods to perform Generalized Cross-Validation, coupling suitable reformulation of key matrices, e.g. those based on Sherman–Morrison–Woodbury formula, with stochastic trace estimation, to approximate the equivalent degrees of freedom of the problem. These solutions permit high computational efficiency also in the context of massive data.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79585054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Retraction: A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations 解双曲型偏微分方程的三次b样条拟插值方法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-07-30 DOI: 10.1080/00207160.2023.2240655
{"title":"Retraction: A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations","authors":"","doi":"10.1080/00207160.2023.2240655","DOIUrl":"https://doi.org/10.1080/00207160.2023.2240655","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87396081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems 求解单调非线性方程和信号恢复问题的新三项共轭梯度算法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-07-23 DOI: 10.1080/00207160.2023.2239947
A. Abubakar, P. Kumam, Jin-kui Liu, Hassan Mohammad, C. Tammer
{"title":"New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems","authors":"A. Abubakar, P. Kumam, Jin-kui Liu, Hassan Mohammad, C. Tammer","doi":"10.1080/00207160.2023.2239947","DOIUrl":"https://doi.org/10.1080/00207160.2023.2239947","url":null,"abstract":"This work presents a new three-term projection algorithm for solving nonlinear monotone equations. The paper is aimed at constructing an efficient and competitive algorithm for finding approximate solutions of nonlinear monotone equations. This is based on a new choice of the conjugate gradient direction which satisfies the sufficient descent condition. The convergence of the algorithm is shown under Lipschitz continuity and monotonicity of the involved operator. Numerical experiments presented in the paper show that the algorithm needs a less number of iterations in comparison with existing algorithms. Furthermore, the proposed algorithm is applied to solve signal recovery problems.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74766572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Viscosity approximation method for split best proximity point and monotone variational inclusion problem 分裂最佳邻近点及单调变分包含问题的粘度近似方法
IF 1.8 4区 数学
International Journal of Computer Mathematics Pub Date : 2023-07-22 DOI: 10.1080/00207160.2023.2239953
S. Husain, Mohd Asad
{"title":"Viscosity approximation method for split best proximity point and monotone variational inclusion problem","authors":"S. Husain, Mohd Asad","doi":"10.1080/00207160.2023.2239953","DOIUrl":"https://doi.org/10.1080/00207160.2023.2239953","url":null,"abstract":"ABSTRACT To address the split best proximity point and monotone variational inclusion problems in real Hilbert spaces, we present and investigate projection and viscosity approximation methods. Under a few reasonable assumptions, we prove some weak and strong convergence theorems for the aforementioned methods. The efficiency of the proposed method is demonstrated by some numerical examples. Some well-known recent results in this area have been improved, generalized, and extended as an outcome of this paper.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85423970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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