J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Approximation of stochastic advection diffusion equations with finite difference scheme Approximation of stochastic advection diffusion equations Namjoo Mehran School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Mohebbian Ali School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran 01 08 2016 4 1 1 18 12 10 2015 04 03 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1571.html

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of \$rm Ithat{o}\$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes, i.e. consistency, stability and convergence, are developed for the stochastic case. It is shown through analysis that the proposed scheme has these properties. Numerical results are given to demonstrate the computational efficiency of the stochastic scheme.

stochastic partial differential equations Consistency Stability Convergence
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper The exponential functions of central-symmetric \$X\$-form matrices The exponential functions of central-symmetric \$X\$-form matrices Sadeghi Amir Department of Mathematics, Islamic Azad University, Robat Karim Branch, Tehran, Iran Shams Solary Maryam Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran 01 08 2016 4 1 19 34 12 08 2016 12 08 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1804.html

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric \$X\$-form. For instance, \$e^{mathbf{A}t}\$, \$t^{mathbf{A}}\$ and \$a^{mathbf{A}t}\$ will be evaluated by the new formulas in this particular structure. Moreover, upper bounds for the explicit relations will be given via subordinate matrix norms. Eventually, some numerical illustrations and applications are also adapted.

central-symmetric matrix matrix function matrix exponential Gamma and Beta matrix functions
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper A path following interior-point algorithm for semidefinite optimization problem based on new kernel function A path following textit{IPMs} for textit{SDO} problem based on new kernel function Djeffal El Amir Department of Mathematics, University of Batna 2, Batna, Algeria Djeffal Lakhdar Department of Mathematics, University of Batna 2, Batna, Algeria 01 08 2016 4 1 35 58 12 08 2016 12 08 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1805.html

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we show that the worst-case iteration bound for our IPM is \$O(6(m+1)^{frac{3m+4}{2(m+1)}}Psi _{0}^{frac{m+2}{2(m+1)}}frac{1}{theta }log frac{nmu ^{0}}{varepsilon })\$, where \$m>4\$.

quadratic programming convex nonlinear programming interior point methods
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Modeling and analysis of a three-component piezoelectric force sensor Modeling and analysis of a three-component piezoelectric force sensor Shao Fu Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada 01 08 2016 4 1 59 78 12 08 2016 12 08 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1806.html

This paper presents a mathematical model for the vibration analysis of a three-component piezoelectric force sensor. The cubic theory of weakly nonlinear electroelasticity is applied to the model for describing the electromechanical coupling effect in the piezoelectric sensing elements which operate in thickness-shear and thickness-stretch vibration modes. Hamilton's principle is used to derive motion and charge equations for the vibration analysis. The model can predict the performance of the force sensor for use in proposed cutting force measurement.

piezoelectric force sensor nonlinear vibration analysis weakly nonlinear electroelasticity
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type Numerical method to solve fourth order SPBVPs Stalin Christy Roja Joseph St. Joseph&#039;s college, Tamilnadu, India Tamilselvan Ayyadurai Bharathidasan University, Tamilnadu, India 01 08 2016 4 1 79 102 12 08 2016 12 08 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1807.html

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  into two subintervals called inner region (boundary layer region) and outer region. The shooting method  is applied to inner region whereas for the outer region, standard finite difference method is applied.  Necessary error estimates are derived. Computational efficiency and accuracy are verified through numerical examples.

singularly perturbed problems fourth order ordinary differential equations boundary value technique asymptotic expansion approximation shooting method finite difference scheme parallel computation
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 Research Paper Dynamics of an eco-epidemic model with stage structure for predator Dynamics of an eco-epidemic model with stage structure for predator Mukherjee Debasis Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata-700063, India 01 08 2016 4 1 103 115 12 08 2016 12 08 2016 Copyright © 2016, دانشگاه گیلان. 2016 https://jmm.guilan.ac.ir/article_1808.html

The predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. The intraspecific competition of infected prey is considered. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibrium is shown. Numerical simulations are carried out to illustrate the obtained results.

prey-predator model stage structure Stability Hopf bifurcation