Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines
133
143
EN
Melis
Zorsahin Gorgulu
Department of Mathematics-Computer, Faculty of Science and Art, Eskisehir Osmangazi University, Eskisehir, Turkey
mzorsahin@ogu.edu.tr
Idris
Dag
Department of Computer Engineering, Faculty of Engineering and Architecture, Eskisehir Osmangazi University, Eskisehir, Turkey
idag@ogu.edu.tr
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.
Exponential B-Spline,Galerkin Method,Crank-Nicolson method,Advection-Diffusion Equation
http://ijm2c.iauctb.ac.ir/article_663819.html
http://ijm2c.iauctb.ac.ir/article_663819_f59bcf4f51ac0619853f81e989bc31bc.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Analytical Solution of Steady State Substrate Concentration of an Immobilized Enzyme Kinetics by Laplace Transform Homotopy Perturbation Method
145
152
EN
Devipriya
Ganeshan
Department of Mathematics,
Stella Maris College,
Chennai - 600 086
devipriyaganeshan@gmail.com
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.
Nonlinear Differential Equation,Approximate Solution,Laplace Transform Homotopy Perturbation Method,numerical simulation
http://ijm2c.iauctb.ac.ir/article_663820.html
http://ijm2c.iauctb.ac.ir/article_663820_4b8b93046f903469c87dd367b69a6894.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Solving Fuzzy Impulsive Fractional Differential Equations by Homotopy Perturbation Method
153
170
EN
Nematallah
Najafi
Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
n.najafi56@yahoo.com
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.
Homotopy Perturbation method,Fuzzy Impulsive Fractional Differential,Generalized Hukuhara differentiability
http://ijm2c.iauctb.ac.ir/article_663821.html
http://ijm2c.iauctb.ac.ir/article_663821_d4de011e5489a60d0f20ea7f06b1afc8.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Steady-State and Dynamic Simulations of Gas Absorption Column Using MATLAB and SIMULINK
171
188
EN
Naved
Siraj
0000-0003-4143-7041
Central Institute of Plastics Engineering and Technology, Bhopal
navedsiraj.rs@amu.ac.in
Abdul
Hakim
Department of Chemical Engineering
Aligarh Muslim University
Aligarh - India
mahakim@rediffmail.com
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.
Sieve Tray,MATLAB,SIMULINK,Mathematical Modeling,Absorption Column
http://ijm2c.iauctb.ac.ir/article_663822.html
http://ijm2c.iauctb.ac.ir/article_663822_2028ef09741eec47c845474c22332361.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method
189
198
EN
Ghasem
Kazemi Gelian
Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran
kazemigelian@yahoo.com
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.
Integral equations,Lane-Emden equation,Sinc collocation method,double exponential transformation.
http://ijm2c.iauctb.ac.ir/article_663823.html
http://ijm2c.iauctb.ac.ir/article_663823_efb31dc80cfcf1d7ffb1498932df68d6.pdf
Islamic Azad University, Central tehran Branch
International Journal of Mathematical Modelling & Computations
2228-6225
2228-6233
8
3 (SUMMER)
2018
08
01
Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
199
206
EN
M.
Karimian
Department mathematics payame noor university of tehran,Iran
malekkarimian@gmail.com
A.
Karimian
Department of Mathematics, University of Tehran, Iran.
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.
Reproducing Kernel Space,Generalized Burgers Equation,Norm Space,Partial Differential Equation
http://ijm2c.iauctb.ac.ir/article_663825.html
http://ijm2c.iauctb.ac.ir/article_663825_5f143c09628fc5b1792b0614fab02b58.pdf