Pub Date : 2022-03-01DOI: 10.17512/jamcm.2022.1.02
Süleyman Çetinkaya, A. Demir
{"title":"Diffusion equation including a local fractional derivative and weighted inner product","authors":"Süleyman Çetinkaya, A. Demir","doi":"10.17512/jamcm.2022.1.02","DOIUrl":"https://doi.org/10.17512/jamcm.2022.1.02","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47935312","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 : 2021-12-01DOI: 10.17512/jamcm.2021.4.04
M. Jemmali, A. Alourani
This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds. MSC 2010: 68M20, 90B35
{"title":"Mathematical model bounds for maximizing the minimum completion time problem","authors":"M. Jemmali, A. Alourani","doi":"10.17512/jamcm.2021.4.04","DOIUrl":"https://doi.org/10.17512/jamcm.2021.4.04","url":null,"abstract":"This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds. MSC 2010: 68M20, 90B35","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46547811","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 : 2021-12-01DOI: 10.17512/jamcm.2021.4.09
Yu. V. Zhernovyi, B. Kopytko
{"title":"Formulas for average transition times between states of the Markov birth-death process","authors":"Yu. V. Zhernovyi, B. Kopytko","doi":"10.17512/jamcm.2021.4.09","DOIUrl":"https://doi.org/10.17512/jamcm.2021.4.09","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44652060","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 : 2021-12-01DOI: 10.17512/jamcm.2021.4.06
M. R. Patel, J. Pandya
This research paper is an attempt to solve the unsteady state convection diffusion one dimension equation. It focuses on the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique. The simulation of the unsteady state convection diffusion problem with a known actual solution is also used to validate both the techniques, respectively, the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique by giving a particular example and solving it using the appropriate, particular technique. It is observed that the numerical scheme is an outstanding deal with the exact solution. Numerical results and graphs are presented for different Peclet numbers. MSC 2010: 65L12, 65M08, 80M12, 80M20, 76Rxx
{"title":"A research study on unsteady state convection diffusion flow with adoption of the finite volume technique","authors":"M. R. Patel, J. Pandya","doi":"10.17512/jamcm.2021.4.06","DOIUrl":"https://doi.org/10.17512/jamcm.2021.4.06","url":null,"abstract":"This research paper is an attempt to solve the unsteady state convection diffusion one dimension equation. It focuses on the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique. The simulation of the unsteady state convection diffusion problem with a known actual solution is also used to validate both the techniques, respectively, the fully implicit hybrid differencing numerical finite volume technique as well as the fully implicit central differencing numerical finite volume technique by giving a particular example and solving it using the appropriate, particular technique. It is observed that the numerical scheme is an outstanding deal with the exact solution. Numerical results and graphs are presented for different Peclet numbers. MSC 2010: 65L12, 65M08, 80M12, 80M20, 76Rxx","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48554994","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 : 2021-12-01DOI: 10.17512/jamcm.2021.4.08
U. Siedlecka, M. Ciesielski
In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated. MSC 2010: 35Q79, 35R11, 44A10, 43A50
{"title":"Analysis of solutions of the 1D fractional Cattaneo heat transfer equation","authors":"U. Siedlecka, M. Ciesielski","doi":"10.17512/jamcm.2021.4.08","DOIUrl":"https://doi.org/10.17512/jamcm.2021.4.08","url":null,"abstract":"In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated. MSC 2010: 35Q79, 35R11, 44A10, 43A50","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41568255","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.06
B. Unyong, Mathialagan Govindaraju, N. Gunasekaran, R. Vadivel
{"title":"Unsteady mixed convection nonlinear radiative Casson nanofluid flow with convective boundary condition, heat source and inclined magnetic field effects","authors":"B. Unyong, Mathialagan Govindaraju, N. Gunasekaran, R. Vadivel","doi":"10.17512/jamcm.2021.3.06","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.06","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45475283","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.07
E. Wegrzyn-Skrzypczak
{"title":"The comparison of results obtained from the continuous and discontinuous Galerkin Method for the thermoelasticity problem","authors":"E. Wegrzyn-Skrzypczak","doi":"10.17512/jamcm.2021.3.07","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.07","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44114439","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.05
Boutheina Tair, H. Guebbai, S. Segni, M. Ghiat
. The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nystr ¨ om method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C 1 [ a , b ] . We have applied the Nystr ¨ om method based on the trapezoidal rule to avoid adding other conditions in order to the approximation method’s convergence. The Nystr ¨ om method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nystr¨om method, some numerical examples will be provided at the end of this work.
{"title":"Solving linear Fredholm integro-differential equation by Nyström method","authors":"Boutheina Tair, H. Guebbai, S. Segni, M. Ghiat","doi":"10.17512/jamcm.2021.3.05","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.05","url":null,"abstract":". The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nystr ¨ om method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C 1 [ a , b ] . We have applied the Nystr ¨ om method based on the trapezoidal rule to avoid adding other conditions in order to the approximation method’s convergence. The Nystr ¨ om method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nystr¨om method, some numerical examples will be provided at the end of this work.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46156045","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.08
Yu. V. Zhernovyi, B. Kopytko
{"title":"Markov reliability models of series systems with redundancy and repair facilities","authors":"Yu. V. Zhernovyi, B. Kopytko","doi":"10.17512/jamcm.2021.3.08","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.08","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42430398","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.04
S. Saha, S. Raut, A. Das
{"title":"Enhancement of turbulent airflow and heat transfer through a rectangular microchannel with different types of baffles","authors":"S. Saha, S. Raut, A. Das","doi":"10.17512/jamcm.2021.3.04","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.04","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42319650","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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