Pub Date : 2023-09-01DOI: 10.17512/jamcm.2023.3.02
Manoj Kumar
Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology
{"title":"An iterative approach for solving fractional order Cauchy reaction-diffusion equations","authors":"Manoj Kumar","doi":"10.17512/jamcm.2023.3.02","DOIUrl":"https://doi.org/10.17512/jamcm.2023.3.02","url":null,"abstract":"Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995592","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 : 2023-09-01DOI: 10.17512/jamcm.2023.3.04
Jarosław Siedlecki
. The colonoscopic electrosurgical polypectomy is a very popular surgical procedure in which the colon polyps are removed. In this work, the mathematical description of the electrical and thermal processes proceeding during this procedure has been proposed. The mathematical model contains the specification of the considered domain’s geometry, the system of the partial differential equations that governs heat transfer in the considered particular sub-domains (i.e. polyp, colon and electrode) with the adequate initial-boundary conditions, the system of the differential equations for determination of the electrical potential distribution in the tissue sub-domains, and the definition of the Arrhenius tissue damage integral. Next, the example results of numerical simulations for the proper and incorrect positions of the polyp in the colon are presented. The conclusions are also provided. The proposed research can be helpful for the surgeons to choose the optimal set parameters of the electric current during the endoscopy procedure. MSC 2010:
{"title":"Electrosurgical resection of colorectal polyps – mathematical modelling of processes during medical treatment","authors":"Jarosław Siedlecki","doi":"10.17512/jamcm.2023.3.04","DOIUrl":"https://doi.org/10.17512/jamcm.2023.3.04","url":null,"abstract":". The colonoscopic electrosurgical polypectomy is a very popular surgical procedure in which the colon polyps are removed. In this work, the mathematical description of the electrical and thermal processes proceeding during this procedure has been proposed. The mathematical model contains the specification of the considered domain’s geometry, the system of the partial differential equations that governs heat transfer in the considered particular sub-domains (i.e. polyp, colon and electrode) with the adequate initial-boundary conditions, the system of the differential equations for determination of the electrical potential distribution in the tissue sub-domains, and the definition of the Arrhenius tissue damage integral. Next, the example results of numerical simulations for the proper and incorrect positions of the polyp in the colon are presented. The conclusions are also provided. The proposed research can be helpful for the surgeons to choose the optimal set parameters of the electric current during the endoscopy procedure. MSC 2010:","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995593","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.06
A. Torii, Paula M.A. Gracite, L. F. Miguel, R. Lopez
. In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement. MSC 2010: 74K10, 65N15
{"title":"A posteriori error estimates for beams with inexact flexural stiffness representation","authors":"A. Torii, Paula M.A. Gracite, L. F. Miguel, R. Lopez","doi":"10.17512/jamcm.2023.2.06","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.06","url":null,"abstract":". In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement. MSC 2010: 74K10, 65N15","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44389247","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.08
Małgorzata Wróbel
. We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space Φ BV ( I ) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces C Φ BV ( I ) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space C Φ BV ( I ) has the Matkowski property.
{"title":"Schramm spaces and composition operators","authors":"Małgorzata Wróbel","doi":"10.17512/jamcm.2023.2.08","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.08","url":null,"abstract":". We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space Φ BV ( I ) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces C Φ BV ( I ) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space C Φ BV ( I ) has the Matkowski property.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42383615","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.07
E. Wegrzyn-Skrzypczak, T. Skrzypczak
. The paper focuses on the numerical modeling of the three-dimensional solidification process of steel using the finite element method (FEM). The model includes and discusses the formation of shrinkage cavities and the influence of the solid phase content on the feeding of the casting through the riser. The analysis assumed a critical value of the solid phase content, at which the transport of liquid phase from the riser to the casting is inter-rupted. The results of numerical simulation are presented to investigate the influence of this factor on the final quality of the casting. The model neglects the fluid motion in the liquid and solid-liquid regions and replaces the influence of the mold with appropriate boundary conditions.
{"title":"Numerical modeling of the solidification process with consideration of shrinkage cavities formation and the influence of solid phase content on the feeding of the casting","authors":"E. Wegrzyn-Skrzypczak, T. Skrzypczak","doi":"10.17512/jamcm.2023.2.07","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.07","url":null,"abstract":". The paper focuses on the numerical modeling of the three-dimensional solidification process of steel using the finite element method (FEM). The model includes and discusses the formation of shrinkage cavities and the influence of the solid phase content on the feeding of the casting through the riser. The analysis assumed a critical value of the solid phase content, at which the transport of liquid phase from the riser to the casting is inter-rupted. The results of numerical simulation are presented to investigate the influence of this factor on the final quality of the casting. The model neglects the fluid motion in the liquid and solid-liquid regions and replaces the influence of the mold with appropriate boundary conditions.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48555445","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.01
Ibrahim Elkott, M. Latif, I. El-Kalla, A. Kader
. In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically. MSC 2010
{"title":"Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative","authors":"Ibrahim Elkott, M. Latif, I. El-Kalla, A. Kader","doi":"10.17512/jamcm.2023.2.01","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.01","url":null,"abstract":". In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically. MSC 2010","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48900477","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.04
A. Mahmud, T. Tanriverdi, K. A. Muhamad, H. Baskonus
. The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics. To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic, periodic, and traveling wave solutions are presented as the results. Consequently, solitary wave solutions are also attained. This study shows that the solutions reported here are distinctive when our findings are contrasted against well-known outcomes. Moreover, realized findings are figured out in 3-dimensional, 2-dimensional, and contour profile graphs for the reader to comprehend their dynamics due to parameter selection. According to the findings, we can conclude that the suggested computational techniques are simple, dynamic, and well-organized. These methods are very functional for numerical calculations of complex nonlinear problems. Our results include a fundamental starting point in understanding physical behavior and the structure of the studied systems.
{"title":"Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation","authors":"A. Mahmud, T. Tanriverdi, K. A. Muhamad, H. Baskonus","doi":"10.17512/jamcm.2023.2.04","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.04","url":null,"abstract":". The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics. To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic, periodic, and traveling wave solutions are presented as the results. Consequently, solitary wave solutions are also attained. This study shows that the solutions reported here are distinctive when our findings are contrasted against well-known outcomes. Moreover, realized findings are figured out in 3-dimensional, 2-dimensional, and contour profile graphs for the reader to comprehend their dynamics due to parameter selection. According to the findings, we can conclude that the suggested computational techniques are simple, dynamic, and well-organized. These methods are very functional for numerical calculations of complex nonlinear problems. Our results include a fundamental starting point in understanding physical behavior and the structure of the studied systems.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67421874","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.02
Dilara Altan Koç
. In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics
{"title":"A numerical scheme for time-fractional fourth-order reaction-diffusion model","authors":"Dilara Altan Koç","doi":"10.17512/jamcm.2023.2.02","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.02","url":null,"abstract":". In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47607909","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.05
F. Shaikh, A. A. Shaikh, E. Hıncal, S. Qureshi
. A mathematical model is developed to study the characteristics of blood flowing through an arterial segment in the presence of a single and a couple of stenoses. The governing equations accompanied by an appropriate choice of initial and boundary conditions are solved numerically by Taylor Galerkin’s time-stepping equation, and the numerical stability is checked. The pressure, velocity, and stream functions have been solved by Cholesky’s method. Furthermore, an in-depth study of the flow pattern reveals the separation of Reynolds number for the 30 and 50% blockage of single stenosis and 30% blockage of multi-stenosis. The present results predict the excess pressure drop across the stenosis site than it does for the inlet of the artery with single and multiple stenosis and the increase in the velocity is observed at the center of the artery.
{"title":"Comparative analysis of numerical simulations of blood flow through the segment of an artery in the presence of stenosis","authors":"F. Shaikh, A. A. Shaikh, E. Hıncal, S. Qureshi","doi":"10.17512/jamcm.2023.2.05","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.05","url":null,"abstract":". A mathematical model is developed to study the characteristics of blood flowing through an arterial segment in the presence of a single and a couple of stenoses. The governing equations accompanied by an appropriate choice of initial and boundary conditions are solved numerically by Taylor Galerkin’s time-stepping equation, and the numerical stability is checked. The pressure, velocity, and stream functions have been solved by Cholesky’s method. Furthermore, an in-depth study of the flow pattern reveals the separation of Reynolds number for the 30 and 50% blockage of single stenosis and 30% blockage of multi-stenosis. The present results predict the excess pressure drop across the stenosis site than it does for the inlet of the artery with single and multiple stenosis and the increase in the velocity is observed at the center of the artery.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48045988","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 : 2023-06-01DOI: 10.17512/jamcm.2023.2.03
R. Kvit
. A composite plate (matrix and reinforcing elements) under conditions of plane deformation is considered. According to the elastic properties, the material of the plate is considered orthotropic with uniformly distributed defects-cracks that do not interact with each other. The geometric characteristics of defects are statistically independent random variables – the half-length and the orientation angle between the defect line and the axis of orthotropy with a larger Young’s modulus. The ratio for the failure loading integral probability distribution function of the composite was obtained. The dependencies of the re-searched composite probability of failure (reliability) for the different number of cracks (plate sizes), different types of loading and various values of the exponential distribution parameter are calculated and investigated graphically.
{"title":"Development of the statistical model failure of orthotropic composite materials","authors":"R. Kvit","doi":"10.17512/jamcm.2023.2.03","DOIUrl":"https://doi.org/10.17512/jamcm.2023.2.03","url":null,"abstract":". A composite plate (matrix and reinforcing elements) under conditions of plane deformation is considered. According to the elastic properties, the material of the plate is considered orthotropic with uniformly distributed defects-cracks that do not interact with each other. The geometric characteristics of defects are statistically independent random variables – the half-length and the orientation angle between the defect line and the axis of orthotropy with a larger Young’s modulus. The ratio for the failure loading integral probability distribution function of the composite was obtained. The dependencies of the re-searched composite probability of failure (reliability) for the different number of cracks (plate sizes), different types of loading and various values of the exponential distribution parameter are calculated and investigated graphically.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49117133","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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