A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation elham afshari Islamic Azad University,khomain Branch author text article 2018 eng In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in the Caputo sense. We propose a new finite difference method for solving time fractional diffu- sion equation. In our method firstly, we transform the Caputo derivative into Riemann-Liovill derivative. The stability and convergence of this method are investigated by a Fourier analysis. We show that this method is uncondition- ally stable and convergent with the convergence order O( 2+h2), where t and h are time and space steps respectively. Finally, a numerical example is given that confirms our theoretical analysis and the behavior of error is examined to verify the order of convergence. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 1 14 http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking Vijaya Laxmi Pikkala Andhra University author Rajesh Pilla Mathematics Department, Andhra University, Visakhapatnam author text article 2018 eng 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. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 17 27 http://ijm2c.iauctb.ac.ir/article_663808_17ddcc16555caed80487bf68adeb0551.pdf An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves Driss Sbibih Department of Mathematics, Faculty of Sciences, University Mohammed First author Bachir Belkhatir LANO Laboratory, University Mohammed First, Oujda, Morocco author text article 2018 eng In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters within a rational cubic Bézier curve should be determined by minimizing a maximum error. We finish by proving and justifying the efficiently of the approaching method with some comparative numerical and graphical examples. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 29 38 http://ijm2c.iauctb.ac.ir/article_663809_d1dd4c38ef1e881719c0e19a3b5d3164.pdf Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse Sunday Fadugba Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria author Temitope Ogunlade Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria author Oluwatayo Ogunmiloro Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria author text article 2018 eng In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the basic reproduction number is less than unity, and the endemic steady state, also, is globally asymptotically stable if the basic reproduction number (R0) is greater than unity. The results obtained from the simulations were analyzed and discussed. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 39 51 http://ijm2c.iauctb.ac.ir/article_663810_d62bac8d56edc602ecabc401078690b5.pdf A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs Pramod Pandey university author text article 2018 eng 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. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 53 60 http://ijm2c.iauctb.ac.ir/article_663811_552a6885603750c8fc676176a7706437.pdf Numerical Solution of The First-Order Evolution Equations by Radial Basis Function Sara Hosseini Qazvin Branch, Islamic Azad University author text article 2018 eng ‎In this work‎, ‎we consider the nonlinear first-order evolution‎ ‎equations‎: ‎$u_t=f(x,t,u,u_x,u_{xx})$ for $0<t<\infty$‎, ‎subject‎ ‎to initial condition $u(x,0)=g(x)$‎, ‎where $u$ is a function of‎ ‎$x$ and $t$ and $f$ is a known analytic function‎. ‎The purpose of‎ ‎this paper is to introduce the method of RBF to existing method‎ ‎in solving nonlinear first-order evolution equations and also the‎ ‎method is implemented in four numerical examples‎. ‎The results‎ ‎reveal that the technique is very effective and simple. International Journal of Mathematical Modelling & Computations Islamic Azad University, Central tehran Branch 2228-6225 8 v. 1 (WINTER) no. 2018 61 66 http://ijm2c.iauctb.ac.ir/article_663812_347d111b5cf75e0f3a38518347268bb6.pdf