Pub Date : 2014-12-25DOI: 10.12941/JKSIAM.2014.18.337
M. Ohm, Hyun Young Lee, J. Shin
In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori L ∞ (L 2 ) error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.
{"title":"HIGHER ORDER DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS","authors":"M. Ohm, Hyun Young Lee, J. Shin","doi":"10.12941/JKSIAM.2014.18.337","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.337","url":null,"abstract":"In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori L ∞ (L 2 ) error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"34 1","pages":"337-350"},"PeriodicalIF":0.6,"publicationDate":"2014-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82292516","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 : 2014-12-25DOI: 10.12941/JKSIAM.2014.18.283
B. Koo, Jisoo Koo, Haoting Song, Hyo-Bin Yoon, Minsu Kim
In this paper we study consumption-labor supply decision of an agent who prepares for retirement at a known time in the future. The agent is assumed to have a preference which is represented by the von Neumann-Morgenstern utility function in which the felicity function has constant relative risk aversion over the composite of consumption and leisure. The composite is obtained by the Cobb-Douglas function. A general problem has been studied by Bodie et al. (2004). We contribute to the literature by deriving the Slutsky equations and conducting comparative statics. In particular, we show that wealth effect can exhibit an interesting property depending upon the time until retirement, as the interest rate increases.
{"title":"HOW TO PREPARE FOR RETIREMENT? OPTIMAL SAVING, LABOR SUPPLY, AND INVESTMENT STRATEGY","authors":"B. Koo, Jisoo Koo, Haoting Song, Hyo-Bin Yoon, Minsu Kim","doi":"10.12941/JKSIAM.2014.18.283","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.283","url":null,"abstract":"In this paper we study consumption-labor supply decision of an agent who prepares for retirement at a known time in the future. The agent is assumed to have a preference which is represented by the von Neumann-Morgenstern utility function in which the felicity function has constant relative risk aversion over the composite of consumption and leisure. The composite is obtained by the Cobb-Douglas function. A general problem has been studied by Bodie et al. (2004). We contribute to the literature by deriving the Slutsky equations and conducting comparative statics. In particular, we show that wealth effect can exhibit an interesting property depending upon the time until retirement, as the interest rate increases.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"5 1","pages":"283-294"},"PeriodicalIF":0.6,"publicationDate":"2014-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80175538","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 : 2014-12-25DOI: 10.12941/JKSIAM.2014.18.305
Chohong Min, G. Yoon
The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the L 2 -orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be O(h 1.5 ) with step size h: In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.
{"title":"CONVERGENCE ANALYSIS ON GIBOU-MIN METHOD FOR THE SCALAR FIELD IN HODGE-HELMHOLTZ DECOMPOSITION","authors":"Chohong Min, G. Yoon","doi":"10.12941/JKSIAM.2014.18.305","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.305","url":null,"abstract":"The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the L 2 -orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be O(h 1.5 ) with step size h: In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"79 1","pages":"305-316"},"PeriodicalIF":0.6,"publicationDate":"2014-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82421160","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 : 2014-12-25DOI: 10.12941/JKSIAM.2014.18.295
D. Choi, Bo-keun Kim, Dae-Eun Lim
We analyze theMMPP/G/1/K queue with a modified state-dependent service rate. The service time of customers upon service initiation is changed if the number of customers in the system reaches a threshold. Then, the changed service time is continued until the system becomes empty completely, and this process is repeated. We analyze this system using an embedded Markov chain and a supplementary variable method, and present the queue length distributions at a customer’s departure epochs and then at an arbitrary time.
{"title":"ANALYSIS OF THE MMPP/G/1/K QUEUE WITH A MODIFIED STATE-DEPENDENT SERVICE RATE","authors":"D. Choi, Bo-keun Kim, Dae-Eun Lim","doi":"10.12941/JKSIAM.2014.18.295","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.295","url":null,"abstract":"We analyze theMMPP/G/1/K queue with a modified state-dependent service rate. The service time of customers upon service initiation is changed if the number of customers in the system reaches a threshold. Then, the changed service time is continued until the system becomes empty completely, and this process is repeated. We analyze this system using an embedded Markov chain and a supplementary variable method, and present the queue length distributions at a customer’s departure epochs and then at an arbitrary time.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"47 1","pages":"295-304"},"PeriodicalIF":0.6,"publicationDate":"2014-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73673364","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 : 2014-12-25DOI: 10.12941/JKSIAM.2014.18.317
A. Elaiw, N. AlShamrani
In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R 0 (the basic infection reproduction number) and R 1 (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle’s invariance principle.
{"title":"GLOBAL ANALYSIS FOR A DELAY - DISTRIBUTED VIRAL INFECTION MODEL WITH ANTIBODIES AND GENERAL NONLINEAR INCIDENCE RATE","authors":"A. Elaiw, N. AlShamrani","doi":"10.12941/JKSIAM.2014.18.317","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.317","url":null,"abstract":"In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters R 0 (the basic infection reproduction number) and R 1 (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle’s invariance principle.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"94 1","pages":"317-335"},"PeriodicalIF":0.6,"publicationDate":"2014-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90520678","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 : 2014-09-25DOI: 10.12941/JKSIAM.2014.18.209
R. Nirmala, K. Balachandran
In this paper, the solution of time fractional telegraph equation is obtained by using Adomain decomposition method and compared with various other method to determine the efficiency of Adomain decomposition method. These methods are used to obtain the series solutions. Finally, results are analysed by plotting the solutions for various fractional orders.
{"title":"ANALYSIS OF SOLUTIONS OF TIME FRACTIONAL TELEGRAPH EQUATION","authors":"R. Nirmala, K. Balachandran","doi":"10.12941/JKSIAM.2014.18.209","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.209","url":null,"abstract":"In this paper, the solution of time fractional telegraph equation is obtained by using Adomain decomposition method and compared with various other method to determine the efficiency of Adomain decomposition method. These methods are used to obtain the series solutions. Finally, results are analysed by plotting the solutions for various fractional orders.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"12 5 1","pages":"209-224"},"PeriodicalIF":0.6,"publicationDate":"2014-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84546597","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 : 2014-09-25DOI: 10.12941/JKSIAM.2014.18.269
Guang-Ri Piao, Hyung-Chen Lee
A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.
{"title":"INTERNAL FEEDBACK CONTROL OF THE BENJAMIN-BONA-MAHONY-BURGERS EQUATION","authors":"Guang-Ri Piao, Hyung-Chen Lee","doi":"10.12941/JKSIAM.2014.18.269","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.269","url":null,"abstract":"A numerical scheme is proposed to control the BBMB (Benjamin-Bona-Mahony-Burgers) equation, and the scheme consists of three steps. Firstly, BBMB equation is converted to a finite set of nonlinear ordinary differential equations by the quadratic B-spline finite element method in spatial. Secondly, the controller is designed based on the linear quadratic regulator (LQR) theory; Finally, the system of the closed loop compensator obtained on the basis of the previous two steps is solved by the backward Euler method. The controlled numerical solutions are obtained for various values of parameters and different initial conditions. Numerical simulations show that the scheme is efficient and feasible.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"22 1","pages":"269-277"},"PeriodicalIF":0.6,"publicationDate":"2014-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87921821","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 : 2014-09-25DOI: 10.12941/JKSIAM.2014.18.225
Dultuya Terbish, Myung-joo Kang
In this work, we discuss segmentation algorithms based on the level set method that incorporates shape prior knowledge. Fundamental segmentation models fail to segment desirable objects from a background when the objects are occluded by others or missing parts of their whole. To overcome these difficulties, we incorporate shape prior knowledge into a new segmentation energy that, uses global and local image information to construct the energy functional. This method improves upon other methods found in the literature and segments images with intensity inhomogeneity, even when images have missing or misleading information due to occlusions, noise, or low-contrast. We consider the case when the shape prior is placed exactly at the locations of the desired objects and the case when the shape prior is placed at arbitrary locations. We test our methods on various images and compare them to other existing methods. Experimental results show that our methods are not only accurate and computationally efficient, but faster than existing methods as well.
{"title":"SEGMENTATION WITH SHAPE PRIOR USING GLOBAL AND LOCAL IMAGE FITTING ENERGY","authors":"Dultuya Terbish, Myung-joo Kang","doi":"10.12941/JKSIAM.2014.18.225","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.225","url":null,"abstract":"In this work, we discuss segmentation algorithms based on the level set method that incorporates shape prior knowledge. Fundamental segmentation models fail to segment desirable objects from a background when the objects are occluded by others or missing parts of their whole. To overcome these difficulties, we incorporate shape prior knowledge into a new segmentation energy that, uses global and local image information to construct the energy functional. This method improves upon other methods found in the literature and segments images with intensity inhomogeneity, even when images have missing or misleading information due to occlusions, noise, or low-contrast. We consider the case when the shape prior is placed exactly at the locations of the desired objects and the case when the shape prior is placed at arbitrary locations. We test our methods on various images and compare them to other existing methods. Experimental results show that our methods are not only accurate and computationally efficient, but faster than existing methods as well.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"32 1","pages":"225-244"},"PeriodicalIF":0.6,"publicationDate":"2014-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81705779","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 : 2014-09-25DOI: 10.12941/JKSIAM.2014.18.279
Namkwon Kim
In this paper, we report a new sharp inequality of interpolation type in R n . This inequality is for controlling weighted average of a function via L n norm of the gradient of a function together with its' certain exponential norm.
{"title":"CERTAIN WEIGHTED MEAN INEQUALITY","authors":"Namkwon Kim","doi":"10.12941/JKSIAM.2014.18.279","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.279","url":null,"abstract":"In this paper, we report a new sharp inequality of interpolation type in R n . This inequality is for controlling weighted average of a function via L n norm of the gradient of a function together with its' certain exponential norm.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"139 1","pages":"279-282"},"PeriodicalIF":0.6,"publicationDate":"2014-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73391367","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 : 2014-09-25DOI: 10.12941/JKSIAM.2014.18.245
S. Devi, M. Prakash
This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The result- ing non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various val- ues of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.
{"title":"STEADY NONLINEAR HYDROMAGNETIC FLOW OVER A STRETCHING SHEET WITH VARIABLE THICKNESS AND VARIABLE SURFACE TEMPERATURE","authors":"S. Devi, M. Prakash","doi":"10.12941/JKSIAM.2014.18.245","DOIUrl":"https://doi.org/10.12941/JKSIAM.2014.18.245","url":null,"abstract":"This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The result- ing non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various val- ues of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"11 1","pages":"245-256"},"PeriodicalIF":0.6,"publicationDate":"2014-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84691629","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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