Journal of Applied Mathematics最新文献

{"title":"A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems","authors":"Anand Shukla, Akhilesh Kumar Singh, Pushpinder Singh","doi":"10.5923/J.AM.20110101.01","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.01","url":null,"abstract":"Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the cru x of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite element method, finite volu me method, finite volu me element method etc. in flu id mechanics. Here we discuss real life problems of fluid engineering solved by various numerical methods .which is very useful for finding solution of those type of governing equation, whose analytical solution are not easily found. Co mputational fluid dynamics is a branch of Engineering and science that,(1) with the help of d igital co mputers, produces quantitative prediction of fluid-flow phenomenon based on those conservation laws governing fluid mot ion. These predictions normally occur under those conditions defined in terms of flow geo metry. Convection- Diffusion Problems arises where fluid flow p lays a significant role .We must account for the effects of convection. Diffusion occurs always alongside convection in nature. The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flo w, in the modeling of semiconductors, and so forth(3). This paper describes several fin ite difference schemes for solving the convection-diffusion equation. Therefore; we examine computation methods to predict comb ined convection- diffusion equation. The convection-diffusion equation is a parabolic partial differential equation combin ing the diffusion equation and the advection equation, which describes physical phenomena where part icles or energy (or other physical quantities) are transferred inside a physical system due to two processes: diffusion and convection. In its simplest form (when the diffusion coefficient and the convection velocity are constant and there are no sources or sinks) the equation takes the form as following: 2 c D c v c t","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250595","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}

{"title":"Self-Similar Flow under the Action of Monochromatic Radiation Behind a Cylindrical MHD Shock in a Non-Ideal Gas","authors":"J. P. Vishwakarma, V. Pandey","doi":"10.5923/J.AM.20120202.06","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.06","url":null,"abstract":"Similarity solutions are obtained for one-dimensional flow under the action of monochromatic radiation behind a cylindrical magnetogasdynamic shock wave propagating in a non-ideal gas in presence of an axial magnetic field. The initial density of the medium and initial magnetic field are assumed to be constant. It is investigated that the presence of the magnetic field or the non-idealness of the gas decays the shock wave, and when the initial magnetic field is strong the non-idealness of the gas affects the velocity and pressure profiles significantly. Also, it is observed that the flow-variables behind the shock are affected significantly, by an increase in the parameter of radiation, when the initial magnetic field is strong. It is, therefore, inferred that the effect of the non-idealness of the gas and of the monochromatic radiation on the shock propagation become more significant when the strength of the initial magnetic field is increased.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"28-33"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250768","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}

{"title":"Mathematical Modelling of HIV/AIDS Dynamics with Treatment and Vertical Transmission","authors":"Abdallah S. Waziri, E. Massawe, O. Makinde","doi":"10.5923/J.AM.20120203.06","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.06","url":null,"abstract":"This paper examines the dynamics of HIV/AIDS with treatment and vertical transmission. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. Local stability of the disease free equilibrium of the model was established by the next generation method. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However, it is shown that using treatment measures (ARVs) and control of the rate of vertical transmission have the effect of reducing the transmission of the disease significantly. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"77-89"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250946","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}

{"title":"Rational Approximation on Closed Curves","authors":"J. I. Mamedkhanov, I. Dadashova","doi":"10.5923/J.AM.20120203.07","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.07","url":null,"abstract":"In this paper, we study a problem of approximation for the classes of functions determined only on the boundary of domain in weighted integral spaces by means of the rational functions of the form (1) where b is a point lying strictly inside the considered curve. Notice that the approximation estimations, generally speaking, coincide with the esti- mations of polynomial approximation for p E classes (Smirnov's class). Approximation problem for the classes of functions de- termined only on the boundary of domain is of great impor- tance alongside with the study of approximation of functions by means of polynomials analytic in the domain G and with some conditions on the boundary Γ . Obviously, it is im- possible in general to approximate such classes of functions by means of polynomials(12). Therefore, various kinds of rational functions or so called generalized polynomials are mostly used in this case as an approximation tool(12). J. I. Mamedkhanov, D. M. Israfilov and I. M. Botchaev investi- gated the approximation problems of functions determined only on the boundary of domain by means of rational func- tions of the form ( ) ( ) ,1 nn R z P z z = for certain classes of curves in terms of uniform metric(1-4). In this paper, we study the approximation problems of a function from the class ( ) , p L ϑ Γ by means of a rational function of the form ( ) ( ) n k nk kn R z a z b − = = −","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"90-93"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251552","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}

{"title":"Complete Classification of BKM Lie Superalgebras Possessing Strictly Imaginary Property","authors":"N. Sthanumoorthy, K. Priyadharsini","doi":"10.5923/J.AM.20120204.02","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.02","url":null,"abstract":"In this paper, comp lete classificat ions of all BKM Lie superalgebras (with fin ite order and infinite order Cartan matrices) possessing Strictly Imaginary Property are given. These classifications also include, in particular, the Monster BKM Lie superalgebra.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"100-115"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251575","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}

{"title":"A Numerical Patching Technique for Singularly Perturbed Nonlinear Differential-Difference Equations with a Negative Shift","authors":"R. Rao, P. Chakravarthy","doi":"10.5923/J.AM.20120202.04","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.04","url":null,"abstract":"In this paper, we present a numerical patching technique for solving singularly perturbed nonlinear differen- tial-difference equation with a small negative shift. The nonlinear problem is converted into a sequence of linear problems by quasilinearization process. After linearization, it is divided into two problems, namely inner region problem and outer region problem. The boundary condition at the cutting point is obtained from the theory of singular perturbations. Using stretching transformation, a modified inner region problem is constructed and is solved by using the upwind finite difference scheme. The outer region problem is solved by a Taylor polynomial approach. We combine the solutions of both problems to obtain an approximate solution of the original problem. The proposed method is iterative on the cutting point. The process is repeated for various choices of the cutting point, until the solution profiles stabilize. Some numerical examples have been solved to demonstrate the applicability of the method. The method is analyzed for stability and convergence.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"43 1","pages":"11-20"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250750","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}

{"title":"Soliton Solution for the BBM and MRLW Equations by Cosine-function Method","authors":"R. Arora, Anoop Kumar","doi":"10.5923/J.AM.20110102.09","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.09","url":null,"abstract":"In this paper, we obtained a traveling wave solution by using cosine-function algorithm for nonlinear partial differential equations. Here, the method is used to obtain the exact solutions for two different types of nonlinear partial dif- ferential equations such as, Benjamin-Bona-Mahony (BBM) equation and Modified Regularized Long Wave (MRLW) equation which are the important soliton equations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"59-61"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250312","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}

{"title":"Umbral Methods, Combinatorial Identities and Harmonic Numbers","authors":"K. Zhukovsky, G. Dattoli","doi":"10.5923/J.AM.20110101.06","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.06","url":null,"abstract":"We analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"46-49"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250272","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}

{"title":"Steady State Solution of a Catastrophic-cum-Restorative M/G/1 Queuing System Using Supplementary Variable Technique","authors":"Rakesh Kumar","doi":"10.5923/J.AM.20110102.10","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.10","url":null,"abstract":"Non- Markovian queuing models have their place in modeling the real life phenomena. In fact, their utility get enhanced when one is not able to get a particular probability distribution for either the inter-arrival times or for the service times. The service times are assumed to have general service time distribution in case of computer communication modeling. Recently, the emphasis is put on the catastrophe modeling and its applications in real situations. Keeping this in view, an M/G/1 queuing model has been developed with catastrophic and restorative effects. The steady-state solution of the model has been obtained using supplementary variable technique. Some queuing models have been obtained as particular cases of this model.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"62-64"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250323","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}

{"title":"Simultaneous Effects of Control Measures on the Transmission Dynamics of Chikungunya Disease","authors":"O. P. Misra, D. Mishra","doi":"10.5923/J.AM.20120204.05","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.05","url":null,"abstract":"Chikungunya is a vector borne communicab le disease which is transmitted in human population through the bite of an infected Aedes-Aegeypti mosquito. In order to study the spread of Chikungunya disease a model has been proposed and analyzed in this paper. In the proposed model the human population and the mosquito population have been divided into three and two classes respectively. For controlling the disease, vector control measures such as, reduction in the breeding of vector population, killing of mosquitoes and isolation of infected humans have been also taken in to account in the model. Linear and non-linear stability analysis of the model has been carried out. Fro m the analysis we have derived a threshold condition involving control reproductive number , and we have found that the disease free equilibriu m point is locally asymptotically stable when and unstable when .We have also proved that a unique endemic equilibriu m point exists and is locally asymptotically stable when . Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number. This study will assist the health department in controlling the spread of Chikungunya disease by introducing the control measures such as increasing the awareness in the society, killing of mosquitoes and isolating the infected individuals.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"124-130"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251638","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}