ORIGINAL_ARTICLE A New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation 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. http://ijm2c.iauctb.ac.ir/article_663807_53c9c99caec4e84548d94062b368e1f6.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 1 14 fractional derivative finite difference method Stability and convergence Fourier analysis time fractional diffusion equation elham afshari math_afshar@yahoo.com true 1 Islamic Azad University,khomain Branch Islamic Azad University,khomain Branch Islamic Azad University,khomain Branch LEAD_AUTHOR
ORIGINAL_ARTICLE Transient Solution of an M/M/1 Variant Working Vacation Queue with Balking 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. http://ijm2c.iauctb.ac.ir/article_663808_17ddcc16555caed80487bf68adeb0551.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 17 27 Queue transient probabilities variant working vacations balking probability generating function continued fractions Laplace transform Vijaya Laxmi Pikkala vijaya_iit2003@yahoo.co.in true 1 Andhra University Andhra University Andhra University LEAD_AUTHOR Rajesh Pilla rajbellman@gmail.com true 2 Mathematics Department, Andhra University, Visakhapatnam Mathematics Department, Andhra University, Visakhapatnam Mathematics Department, Andhra University, Visakhapatnam AUTHOR
ORIGINAL_ARTICLE An Optimal G^2-Hermite Interpolation by Rational Cubic Bézier Curves 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. http://ijm2c.iauctb.ac.ir/article_663809_d1dd4c38ef1e881719c0e19a3b5d3164.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 29 38 Hermite interpolation Rational curve G^2 continuity Geometric conditions Optimization Driss Sbibih sbibih@yahoo.fr true 1 Department of Mathematics, Faculty of Sciences, University Mohammed First Department of Mathematics, Faculty of Sciences, University Mohammed First Department of Mathematics, Faculty of Sciences, University Mohammed First LEAD_AUTHOR Bachir Belkhatir bachirbelkhatir@yahoo.fr true 2 LANO Laboratory, University Mohammed First, Oujda, Morocco LANO Laboratory, University Mohammed First, Oujda, Morocco LANO Laboratory, University Mohammed First, Oujda, Morocco AUTHOR
ORIGINAL_ARTICLE Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse 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. http://ijm2c.iauctb.ac.ir/article_663810_d62bac8d56edc602ecabc401078690b5.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 39 51 Global stability Local stability Lyapunov Optimal Control Pontryagin maximum principle Sunday Fadugba sunday.fadugba@eksu.edu.ng true 1 Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria LEAD_AUTHOR Temitope Ogunlade topsmatic@gmail.com true 2 Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria Department of Mathematics, Ekiti-State University (EKSU), Ado-Ekiti. Ekiti-State, Nigeria AUTHOR Oluwatayo Ogunmiloro oluwatayo.ogunmiloro@eksu.edu.ng true 3 Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria Department of Mathematics, Faculty of Science, Ekiti State University, Nigeria AUTHOR
ORIGINAL_ARTICLE A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs 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. http://ijm2c.iauctb.ac.ir/article_663811_552a6885603750c8fc676176a7706437.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 53 60 Boundary Value Problem Difference Method Third Order Convergence Third Order Differential Equation Pramod Pandey pramod_10p@hotmail.com true 1 university university university LEAD_AUTHOR
ORIGINAL_ARTICLE Numerical Solution of The First-Order Evolution Equations by Radial Basis Function ‎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. http://ijm2c.iauctb.ac.ir/article_663812_347d111b5cf75e0f3a38518347268bb6.pdf 2018-01-01T11:23:20 2020-03-30T11:23:20 61 66 ‎First-order evolution equations ‎Radial basis‎ ‎function Newton&#039;s method nonlinear equations‎ Sara Hosseini s_hosseini66@yahoo.com true 1 Qazvin Branch, Islamic Azad University Qazvin Branch, Islamic Azad University Qazvin Branch, Islamic Azad University LEAD_AUTHOR