Pub Date : 2023-05-04DOI: 10.1080/00207160.2023.2210694
Xue Wang, Yimeng Zhang, H. Rui
In this paper, we propose and analyse pressure-correction schemes based on marker and cell (MAC) method for the linear Stokes–Biot system with a fixed interface. The implicit backward Euler scheme for the time discretization is used, whereas the coupling terms are treated explicitly. These schemes are computationally efficient in that we only solve two decoupled problems. And for Stokes equations, we solve one vector-valued elliptic equation and one scalar-value Poisson equation per time step. These methods have optimal order without the incompressibility constraint of the Stokes system. We prove rigorously that they are unconditionally stable and present the numerical experiments to show their performance.
{"title":"A stable pressure-correction MAC scheme for the fluid-Poroelastic material interaction problem","authors":"Xue Wang, Yimeng Zhang, H. Rui","doi":"10.1080/00207160.2023.2210694","DOIUrl":"https://doi.org/10.1080/00207160.2023.2210694","url":null,"abstract":"In this paper, we propose and analyse pressure-correction schemes based on marker and cell (MAC) method for the linear Stokes–Biot system with a fixed interface. The implicit backward Euler scheme for the time discretization is used, whereas the coupling terms are treated explicitly. These schemes are computationally efficient in that we only solve two decoupled problems. And for Stokes equations, we solve one vector-valued elliptic equation and one scalar-value Poisson equation per time step. These methods have optimal order without the incompressibility constraint of the Stokes system. We prove rigorously that they are unconditionally stable and present the numerical experiments to show their performance.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"37 1","pages":"1683 - 1701"},"PeriodicalIF":1.8,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85439895","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}
Pub Date : 2023-04-28DOI: 10.1080/00207160.2023.2208681
B. Gunes, Hakki Duru
This paper aims to establish the finite difference scheme on Bakhvalov-type mesh for the singularly perturbed pseudo-parabolic problems with time-delay. Using the energy estimates, the bounds of the solution are investigated. An error analysis is derived in the discrete energy norm and the almost second order convergence is obtained. The reliability of the suggested method is displayed by means of a numerical example.
{"title":"A computational method for the singularly perturbed delay pseudo-parabolic differential equations on adaptive mesh","authors":"B. Gunes, Hakki Duru","doi":"10.1080/00207160.2023.2208681","DOIUrl":"https://doi.org/10.1080/00207160.2023.2208681","url":null,"abstract":"This paper aims to establish the finite difference scheme on Bakhvalov-type mesh for the singularly perturbed pseudo-parabolic problems with time-delay. Using the energy estimates, the bounds of the solution are investigated. An error analysis is derived in the discrete energy norm and the almost second order convergence is obtained. The reliability of the suggested method is displayed by means of a numerical example.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"55 1","pages":"1667 - 1682"},"PeriodicalIF":1.8,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80017573","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}
Pub Date : 2023-04-26DOI: 10.1080/00207160.2023.2207677
A. Singh, R. Maurya, V. Singh
The current paper develops and analyzes a numerical scheme for the space–time fractional stochastic nonlinear diffusion wave equations. The implicit scheme is based on the matrix transform technique for discretizing the Riesz-space fractional derivative, -order approximation to the Caputo-fractional derivative in time and Taylor's series method to linearize the nonlinear source term, and has been successfully applied to solve a class of nonlinear fractional diffusion wave equation. We prove that the implicit scheme is convergent with β-order in space and order in time, respectively. The optimum error estimates in the temporal-spatial direction and unconditional stability of the implicit scheme have been theoretically investigated. Moreover, several specific numerical experiments confirm the consistency and high efficacy of the provided algorithms, which minimizes the computational costs.
{"title":"Analysis of a robust implicit scheme for space–time fractional stochastic nonlinear diffusion wave model","authors":"A. Singh, R. Maurya, V. Singh","doi":"10.1080/00207160.2023.2207677","DOIUrl":"https://doi.org/10.1080/00207160.2023.2207677","url":null,"abstract":"The current paper develops and analyzes a numerical scheme for the space–time fractional stochastic nonlinear diffusion wave equations. The implicit scheme is based on the matrix transform technique for discretizing the Riesz-space fractional derivative, -order approximation to the Caputo-fractional derivative in time and Taylor's series method to linearize the nonlinear source term, and has been successfully applied to solve a class of nonlinear fractional diffusion wave equation. We prove that the implicit scheme is convergent with β-order in space and order in time, respectively. The optimum error estimates in the temporal-spatial direction and unconditional stability of the implicit scheme have been theoretically investigated. Moreover, several specific numerical experiments confirm the consistency and high efficacy of the provided algorithms, which minimizes the computational costs.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"254 1","pages":"1625 - 1645"},"PeriodicalIF":1.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75762860","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}
Pub Date : 2023-04-26DOI: 10.1080/00207160.2023.2207389
Najeeb Abdulaleem
In this paper, a class of E-differentiable multiobjective programming with multiple objective functions and with both inequality and equality constraints is considered. The so-called E-Karush–Kuhn–Tucker necessary optimality conditions for a (weak LS-Pareto) LS-Pareto solution are established for the considered E-differentiable vector optimization problem with the multiple interval-valued objective functions. Also several sufficient optimality conditions for both LU and LS order relations are derived for such interval-valued vector optimization problems under (generalized) E-invexity hypotheses.
{"title":"Optimality conditions for a class of E-differentiable vector optimization problems with interval-valued objective functions under E-invexity","authors":"Najeeb Abdulaleem","doi":"10.1080/00207160.2023.2207389","DOIUrl":"https://doi.org/10.1080/00207160.2023.2207389","url":null,"abstract":"In this paper, a class of E-differentiable multiobjective programming with multiple objective functions and with both inequality and equality constraints is considered. The so-called E-Karush–Kuhn–Tucker necessary optimality conditions for a (weak LS-Pareto) LS-Pareto solution are established for the considered E-differentiable vector optimization problem with the multiple interval-valued objective functions. Also several sufficient optimality conditions for both LU and LS order relations are derived for such interval-valued vector optimization problems under (generalized) E-invexity hypotheses.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"5 1","pages":"1601 - 1624"},"PeriodicalIF":1.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79075870","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}
Pub Date : 2023-04-26DOI: 10.1080/00207160.2023.2208236
Juan Li, Hong Sun, Xuan Zhao
The backward differential formulas of order 3-5 (BDF3-5) are applied to simulate the molecular beam epitaxial (MBE) model with slop selection. The fully implicit BDF3-5 schemes are uniquely solvable under an estimated time-step requirement. We prove that the schemes conserve the modified discrete energy dissipation laws by utilizing the discrete gradient structures of BDF3-5 formulas. Furthermore, we present a new convolution inequality to handle the nonlinear term for the error estimate. More importantly, the norm convergence analysis of the BDF3-5 schemes are proved rigorously without the assumption of Lipschitz boundedness. Numerical examples are shown to verify the efficiency and the accuracy of the developed schemes.
{"title":"Energy stable and convergent BDF3-5 schemes for the molecular beam epitaxial model with slope selection","authors":"Juan Li, Hong Sun, Xuan Zhao","doi":"10.1080/00207160.2023.2208236","DOIUrl":"https://doi.org/10.1080/00207160.2023.2208236","url":null,"abstract":"The backward differential formulas of order 3-5 (BDF3-5) are applied to simulate the molecular beam epitaxial (MBE) model with slop selection. The fully implicit BDF3-5 schemes are uniquely solvable under an estimated time-step requirement. We prove that the schemes conserve the modified discrete energy dissipation laws by utilizing the discrete gradient structures of BDF3-5 formulas. Furthermore, we present a new convolution inequality to handle the nonlinear term for the error estimate. More importantly, the norm convergence analysis of the BDF3-5 schemes are proved rigorously without the assumption of Lipschitz boundedness. Numerical examples are shown to verify the efficiency and the accuracy of the developed schemes.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"86 1","pages":"1646 - 1665"},"PeriodicalIF":1.8,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83750322","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}
Pub Date : 2023-04-20DOI: 10.1080/00207160.2023.2205963
Sudhir Kumar, R. C. Mittal, Ram Jiwari
We, the Editors and Publisher of International Journal of Computer Mathematics have retracted the following article: Sudhir Kumar, R.C. Mittal & Ram Jiwari (2023) A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations, International Journal of Computer Mathematics, DOI: 10.1080/00207160.2023.2205963 Since publication, significant concerns have been raised about the fact that this article has substantial overlap with the following article which was not acknowledged, particularly in Sections 1-4 where there were verbatim sentences and sentence fragments: Mittal, R. C., Kumar, S., & Jiwari, R. (2021). A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction-diffusion models. Engineering with Computers, 1-17 https://doi.org/10.1007/s00366-020-01278-3. Upon query, the authors were not able to address the concerns with their paper or provide a satisfactory explanation for this significant level of overlap. As this is a serious breach of our Editorial Policies, we are retracting the article from the journal. The authors do not agree with the retraction. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.
{"title":"RETRACTED ARTICLE: A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations","authors":"Sudhir Kumar, R. C. Mittal, Ram Jiwari","doi":"10.1080/00207160.2023.2205963","DOIUrl":"https://doi.org/10.1080/00207160.2023.2205963","url":null,"abstract":"We, the Editors and Publisher of International Journal of Computer Mathematics have retracted the following article: Sudhir Kumar, R.C. Mittal & Ram Jiwari (2023) A cubic B-spline quasi-interpolation method for solving hyperbolic partial differential equations, International Journal of Computer Mathematics, DOI: 10.1080/00207160.2023.2205963 Since publication, significant concerns have been raised about the fact that this article has substantial overlap with the following article which was not acknowledged, particularly in Sections 1-4 where there were verbatim sentences and sentence fragments: Mittal, R. C., Kumar, S., & Jiwari, R. (2021). A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction-diffusion models. Engineering with Computers, 1-17 https://doi.org/10.1007/s00366-020-01278-3. Upon query, the authors were not able to address the concerns with their paper or provide a satisfactory explanation for this significant level of overlap. As this is a serious breach of our Editorial Policies, we are retracting the article from the journal. The authors do not agree with the retraction. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"9 1","pages":"1580 - 1600"},"PeriodicalIF":1.8,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84640093","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}
Pub Date : 2023-04-20DOI: 10.1080/00207160.2023.2205962
Lin Zhang, Y. Ge, Xiaojia Yang, Yagang Zhang
We focus on high-accuracy and stable numerical methods for the time-dependent nonlinear advection-diffusion-reaction problems in this work. A novel fourth-order fully implicit compact difference scheme is derived, in which we make use of the fourth-order compact formulas to discretize the diffusion terms, the fourth-order Padé formulas to compute the nonlinear advection terms, and the fourth-order backward differencing formula to approximate the time derivative term. Convergence and stability of the new scheme are analysed by the energy method. On the basis of the novel scheme, a multigrid algorithm is established such that a time advancement algorithm for solving these nonlinear problems are obtained. We provide various numerical experiments to verify the performances of the proposed scheme including the reliability, stability and computational efficiency. And the results obtained by our method show it is more accurate than most same kind schemes reported in the literature.
{"title":"High accuracy compact difference and multigrid methods for two-dimensional time-dependent nonlinear advection-diffusion-reaction problems","authors":"Lin Zhang, Y. Ge, Xiaojia Yang, Yagang Zhang","doi":"10.1080/00207160.2023.2205962","DOIUrl":"https://doi.org/10.1080/00207160.2023.2205962","url":null,"abstract":"We focus on high-accuracy and stable numerical methods for the time-dependent nonlinear advection-diffusion-reaction problems in this work. A novel fourth-order fully implicit compact difference scheme is derived, in which we make use of the fourth-order compact formulas to discretize the diffusion terms, the fourth-order Padé formulas to compute the nonlinear advection terms, and the fourth-order backward differencing formula to approximate the time derivative term. Convergence and stability of the new scheme are analysed by the energy method. On the basis of the novel scheme, a multigrid algorithm is established such that a time advancement algorithm for solving these nonlinear problems are obtained. We provide various numerical experiments to verify the performances of the proposed scheme including the reliability, stability and computational efficiency. And the results obtained by our method show it is more accurate than most same kind schemes reported in the literature.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"94 1","pages":"1552 - 1579"},"PeriodicalIF":1.8,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90992635","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}
Pub Date : 2023-04-17DOI: 10.1080/00207160.2023.2203787
M. Abukhaled, S. Khuri
{"title":"RLC electric circuit model of fractional order: A Green's function approach","authors":"M. Abukhaled, S. Khuri","doi":"10.1080/00207160.2023.2203787","DOIUrl":"https://doi.org/10.1080/00207160.2023.2203787","url":null,"abstract":"","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"67 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76844243","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}
Pub Date : 2023-04-17DOI: 10.1080/00207160.2023.2202996
As the stringency of the peer review process is core to the integrity of the publication process, the Editor and Publisher have taken the decision to retract the article. The journal has not confirmed if the authors were aware of this compromised peer review process. The journal is committed to correcting the scientific record and will fully cooperate with any institutional investigations into this matter. The authors have been informed of this decision.
{"title":"Retraction: Mathematical Techniques and Applications of Linear Differential Equation","authors":"","doi":"10.1080/00207160.2023.2202996","DOIUrl":"https://doi.org/10.1080/00207160.2023.2202996","url":null,"abstract":"As the stringency of the peer review process is core to the integrity of the publication process, the Editor and Publisher have taken the decision to retract the article. The journal has not confirmed if the authors were aware of this compromised peer review process. The journal is committed to correcting the scientific record and will fully cooperate with any institutional investigations into this matter. The authors have been informed of this decision.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"47 1","pages":"1418 - 1418"},"PeriodicalIF":1.8,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86863847","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}
Pub Date : 2023-04-17DOI: 10.1080/00207160.2023.2203786
Jianyu Wang, Chunhua Fang, Gui-yu Zhang
In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels. The purpose is to solve the equations by Kummer hypergeometric and Gamma functions for solving the modified moments, where the modified moments are transformed from the integration interval [0,x] to the interval [−1,1]. The detailed collocation procedure is provided and the effectiveness of these algorithms are proved by convergence analysis and numerical experiments. Further, numerical examples are used to prove that the direct linear interpolation collocation method and the direct high order interpolation collocation method are also effective for solving highly oscillatory equations without weakly singularities.
{"title":"Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels","authors":"Jianyu Wang, Chunhua Fang, Gui-yu Zhang","doi":"10.1080/00207160.2023.2203786","DOIUrl":"https://doi.org/10.1080/00207160.2023.2203786","url":null,"abstract":"In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels. The purpose is to solve the equations by Kummer hypergeometric and Gamma functions for solving the modified moments, where the modified moments are transformed from the integration interval [0,x] to the interval [−1,1]. The detailed collocation procedure is provided and the effectiveness of these algorithms are proved by convergence analysis and numerical experiments. Further, numerical examples are used to prove that the direct linear interpolation collocation method and the direct high order interpolation collocation method are also effective for solving highly oscillatory equations without weakly singularities.","PeriodicalId":13911,"journal":{"name":"International Journal of Computer Mathematics","volume":"24 1","pages":"1532 - 1551"},"PeriodicalIF":1.8,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87393662","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}
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