Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation 1 14 EN elham afshari Islamic Azad University,khomain Branch math_afshar@yahoo.com In this paper, a time fractional diffusion equation on a finite domain is con-<br /> sidered. The time fractional diffusion equation is obtained from the standard<br /> diffusion equation by replacing the first order time derivative by a fractional<br /> derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In<br /> equation that we consider the time fractional derivative is in the Caputo sense.<br /> We propose a new finite difference method for solving time fractional diffu-<br /> sion equation. In our method firstly, we transform the Caputo derivative into<br /> Riemann-Liovill derivative. The stability and convergence of this method are<br /> investigated by a Fourier analysis. We show that this method is uncondition-<br /> ally stable and convergent with the convergence order O( 2+h2), where t and<br /> h are time and space steps respectively. Finally, a numerical example is given<br /> that confirms our theoretical analysis and the behavior of error is examined<br /> to verify the order of convergence. fractional derivative,finite difference method,Stability and convergence,Fourier analysis,time fractional diffusion equation http://ijm2c.iauctb.ac.ir/article_663807.html http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking 17 27 EN Vijaya Laxmi Pikkala Andhra University vijaya_iit2003@yahoo.co.in Rajesh Pilla Mathematics Department, Andhra University, Visakhapatnam rajbellman@gmail.com This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability \$b\$ or balk with \$bar{b} = 1-b\$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed to be exponentially distributed and are mutually independent. We have obtained the transient-state probabilities in terms of modified Bessel function of the first kind by employing probability generating function, continued fractions and Laplace transform. In addition, we have also obtained some other performance measures. Queue,transient probabilities,variant working vacations,balking,probability generating function,continued fractions,Laplace transform http://ijm2c.iauctb.ac.ir/article_663808.html http://ijm2c.iauctb.ac.ir/article_663808_17ddcc16555caed80487bf68adeb0551.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves 29 38 EN Driss Sbibih Department of Mathematics, Faculty of Sciences, University Mohammed First sbibih@yahoo.fr Bachir Belkhatir LANO Laboratory, University Mohammed First, Oujda, Morocco bachirbelkhatir@yahoo.fr In this paper, we study a geometric G^2 Hermite interpolation by planar rational<br /> cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures<br /> interpolated per each rational segment. We give the necessary and the sufficient<br /> intrinsic geometric conditions for two C^2 parametric curves to be connected with G2<br /> continuity. Locally, the free parameters within a rational cubic Bézier curve should<br /> be determined by minimizing a maximum error. We finish by proving and justifying<br /> the efficiently of the approaching method with some comparative numerical and<br /> graphical examples. Hermite interpolation,Rational curve,G^2 continuity,Geometric conditions,Optimization http://ijm2c.iauctb.ac.ir/article_663809.html http://ijm2c.iauctb.ac.ir/article_663809_d1dd4c38ef1e881719c0e19a3b5d3164.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse 39 51 EN Sunday Emmanuel Fadugba Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria sunday.fadugba@eksu.edu.ng Temitope Ogunlade Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria topsmatic@gmail.com Oluwatayo Ogunmiloro Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria oluwatayo.ogunmiloro@eksu.edu.ng In this paper, we studied and formulated the relapsed SIR model of a constant size<br /> population with standard incidence rate. Also, the optimal control problem with treatment<br /> and vaccination as controls, subject to the model is formulated. The analysis carried out<br /> on the model, clearly showed that the infection free steady state is globally asymptotically<br /> stable if the basic reproduction number is less than unity, and the endemic steady state,<br /> also, is globally asymptotically stable if the basic reproduction number (R0) is greater than<br /> unity. The results obtained from the simulations were analyzed and discussed. Global stability,Local stability,Lyapunov,Optimal Control,Pontryagin maximum principle http://ijm2c.iauctb.ac.ir/article_663810.html http://ijm2c.iauctb.ac.ir/article_663810_d62bac8d56edc602ecabc401078690b5.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs 53 60 EN Pramod Pandey university pramod_10p@hotmail.com In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply high accuracy and efficiency of the method. Boundary Value Problem,Difference Method,Third Order Convergence,Third Order Differential Equation http://ijm2c.iauctb.ac.ir/article_663811.html http://ijm2c.iauctb.ac.ir/article_663811_552a6885603750c8fc676176a7706437.pdf
Islamic Azad University, Central Tehran Branch International Journal of Mathematical Modelling & Computations 2228-6225 2228-6233 8 1 (WINTER) 2018 01 01 Numerical Solution of The First-Order Evolution Equations by Radial Basis Function 61 66 EN Sara Hosseini Qazvin Branch, Islamic Azad University s_hosseini66@yahoo.com ‎In this work‎, ‎we consider the nonlinear first-order evolution‎<br /> ‎equations‎: ‎\$u_t=f(x,t,u,u_x,u_{xx})\$ for \$0<t<infty\$‎, ‎subject‎<br /> ‎to initial condition \$u(x,0)=g(x)\$‎, ‎where \$u\$ is a function of‎<br /> ‎\$x\$ and \$t\$ and \$f\$ is a known analytic function‎. ‎The purpose of‎<br /> ‎this paper is to introduce the method of RBF to existing method‎<br /> ‎in solving nonlinear first-order evolution equations and also the‎ ‎method is implemented in four numerical examples‎. ‎The results‎<br /> ‎reveal that the technique is very effective and simple. ‎First-order evolution equations,‎Radial basis‎ ‎function,Newton's method,nonlinear equations‎ http://ijm2c.iauctb.ac.ir/article_663812.html http://ijm2c.iauctb.ac.ir/article_663812_347d111b5cf75e0f3a38518347268bb6.pdf