2018
8
3
31
0
Galerkin Method for the Numerical Solution of the AdvectionDiffusion Equation by Using Exponential Bsplines
2
2
In this paper, the exponential Bspline functions are used for the numerical solution of the advectiondiffusion 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.
1

133
143


Melis
Zorsahin Gorgulu
Department of MathematicsComputer, Faculty of Science and Art, Eskisehir Osmangazi University, Eskisehir, Turkey
Department of MathematicsComputer, Faculty
Iran
mzorsahin@ogu.edu.tr


Idris
Dag
Department of Computer Engineering, Faculty of Engineering and Architecture, Eskisehir Osmangazi University, Eskisehir, Turkey
Department of Computer Engineering, Faculty
Iran
idag@ogu.edu.tr
Exponential BSpline
Galerkin Method
CrankNicolson method
AdvectionDiffusion Equation
Analytical Solution of Steady State Substrate Concentration of an Immobilized Enzyme Kinetics by Laplace Transform Homotopy Perturbation Method
2
2
The nonlinear dynamical system modeling the immobilized enzyme kinetics with MichaelisMenten 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.
1

145
152


Devipriya
Ganeshan
Department of Mathematics,
Stella Maris College,
Chennai  600 086
Department of Mathematics,
Stella Maris
Iran
devipriyaganeshan@gmail.com
Nonlinear Differential Equation
Approximate Solution
Laplace Transform Homotopy Perturbation Method
numerical simulation
Solving Fuzzy Impulsive Fractional Differential Equations by Homotopy Perturbation Method
2
2
In this paper, we study semianalytical 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.
1

153
170


Nematallah
Najafi
Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
Department of Mathematics, Islamic Azad University
Iran
n.najafi56@yahoo.com
Homotopy Perturbation method
Fuzzy Impulsive Fractional Differential
Generalized Hukuhara differentiability
SteadyState and Dynamic Simulations of Gas Absorption Column Using MATLAB and SIMULINK
2
2
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.
1

171
188


Naved
Siraj
Central Institute of Plastics Engineering and Technology, Bhopal
Central Institute of Plastics Engineering
Iran
navedsiraj.rs@amu.ac.in


Abdul
Hakim
Department of Chemical Engineering
Aligarh Muslim University
Aligarh  India
Department of Chemical Engineering
Aligarh
Iran
mahakim@rediffmail.com
Sieve Tray
MATLAB
SIMULINK
Mathematical Modeling
Absorption Column
Numerical Solution of the LaneEmden Equation Based on DE Transformation via Sinc Collocation Method
2
2
In this paper, numerical solution of general LaneEmden 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 runtime, computational cost and implementation are discussed.
1

189
198


Ghasem
Kazemi Gelian
Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran
Department of Mathematics, Shirvan Branch,
Iran
kazemigelian@yahoo.com
Integral equations
LaneEmden equation
Sinc collocation method
double exponential transformation.
Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
2
2
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.
1

199
206


M.
Karimian
Department mathematics payame noor university of tehran,Iran
Department mathematics payame noor university
Iran
malekkarimian@gmail.com


A.
Karimian
Department of Mathematics, University of Tehran, Iran.
Department of Mathematics, University of
Iran
Reproducing Kernel Space
Generalized Burgers Equation
Norm Space
Partial Differential Equation