ORIGINAL_ARTICLE Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies. http://ijm2c.iauctb.ac.ir/article_663819_f59bcf4f51ac0619853f81e989bc31bc.pdf 2018-08-01 133 143 Exponential B-Spline Galerkin Method Crank-Nicolson method Advection-Diffusion Equation Melis Zorsahin Gorgulu mzorsahin@ogu.edu.tr 1 Department of Mathematics-Computer, Faculty of Science and Art, Eskisehir Osmangazi University, Eskisehir, Turkey LEAD_AUTHOR Idris Dag idag@ogu.edu.tr 2 Department of Computer Engineering, Faculty of Engineering and Architecture, Eskisehir Osmangazi University, Eskisehir, Turkey AUTHOR
ORIGINAL_ARTICLE Analytical Solution of Steady State Substrate Concentration of an Immobilized Enzyme Kinetics by Laplace Transform Homotopy Perturbation Method The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the exact solution or enabling to built the approximate solution of the problem. Numerical solutions are obtained and the results are discussed graphically. The method allows to determine the solution in form of the continuous function, which is significant for the analysis of the steady state dimensionless substrate concentration with dimensionless distance on the different support materials. http://ijm2c.iauctb.ac.ir/article_663820_4b8b93046f903469c87dd367b69a6894.pdf 2018-08-01 145 152 Nonlinear Differential Equation Approximate Solution Laplace Transform Homotopy Perturbation Method numerical simulation Devipriya Ganeshan devipriyaganeshan@gmail.com 1 Department of Mathematics, Stella Maris College, Chennai - 600 086 LEAD_AUTHOR
ORIGINAL_ARTICLE Solving Fuzzy Impulsive Fractional Differential Equations by Homotopy Perturbation Method In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show that the approximate solution convergent to the exact solution. Some examples indicate that this method can be easily applied to many linear and nonlinear problems. http://ijm2c.iauctb.ac.ir/article_663821_d4de011e5489a60d0f20ea7f06b1afc8.pdf 2018-08-01 153 170 Homotopy Perturbation method Fuzzy Impulsive Fractional Differential Generalized Hukuhara differentiability Nematallah Najafi n.najafi56@yahoo.com 1 Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran LEAD_AUTHOR
ORIGINAL_ARTICLE Steady-State and Dynamic Simulations of Gas Absorption Column Using MATLAB and SIMULINK Separation is one of the most important process in all the chemical industries and the gas absorption is the simplest example of separation process which is generally used for the absorption of dilute components from a gaseous mixture. In the present work, a dynamic system of mathematical equation (algebraic and differential) is modeled to predict the behavior of the absorption column using matrix algebra. The dynamic model was programmed using MATLAB/SIMULINK and S – function was used for building user define blocks to find out the liquid and the gas composition using the standard MATLAB ode45 solver. As a case study, fermentation process is taken as an example to separate CO2 from a mixture of alcohol and CO2 in a tray gas absorber using water as absorbent. The steady state solution was first solved to give the initial condition for the dynamic analysis. Dynamic outcomes for stage compositions was figure out for step changes in the vapor and liquid feed compositions. The model results show good agreement with the practical situation and also compared favorably with results obtained by Bequette. With this work, we are able to provide a readily available simulation that can be used as a test bed for advanced process monitoring. http://ijm2c.iauctb.ac.ir/article_663822_2028ef09741eec47c845474c22332361.pdf 2018-08-01 171 188 Sieve Tray MATLAB SIMULINK Mathematical Modeling Absorption Column Naved Siraj navedsiraj.rs@amu.ac.in 1 Central Institute of Plastics Engineering and Technology, Bhopal LEAD_AUTHOR Abdul Hakim mahakim@rediffmail.com 2 Department of Chemical Engineering Aligarh Muslim University Aligarh - India AUTHOR
ORIGINAL_ARTICLE Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed. http://ijm2c.iauctb.ac.ir/article_663823_efb31dc80cfcf1d7ffb1498932df68d6.pdf 2018-08-01 189 198 Integral equations‎ Lane-Emden equation Sinc collocation‎ ‎method‎ ‎double exponential transformation.‎ Ghasem Kazemi Gelian kazemigelian@yahoo.com 1 Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran LEAD_AUTHOR
ORIGINAL_ARTICLE Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved. http://ijm2c.iauctb.ac.ir/article_663825_5f143c09628fc5b1792b0614fab02b58.pdf 2018-08-01 199 206 Reproducing Kernel Space Generalized Burgers Equation Norm Space Partial Differential Equation M. Karimian malekkarimian@gmail.com 1 Department mathematics payame noor university of tehran,Iran LEAD_AUTHOR A. Karimian 2 Department of Mathematics, University of Tehran, Iran. AUTHOR