Galerkin Method for the Numerical Solution of the Advection-Diffusion Equation by Using Exponential B-splines
Melis
Zorsahin Gorgulu
Department of Mathematics-Computer, Faculty of Science and Art, Eskisehir Osmangazi University, Eskisehir, Turkey
author
Idris
Dag
Department of Computer Engineering, Faculty of Engineering and Architecture, Eskisehir Osmangazi University, Eskisehir, Turkey
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
133
143
http://ijm2c.iauctb.ac.ir/article_663819_f59bcf4f51ac0619853f81e989bc31bc.pdf
Analytical Solution of Steady State Substrate Concentration of an Immobilized Enzyme Kinetics by Laplace Transform Homotopy Perturbation Method
Devipriya
Ganeshan
Department of Mathematics,
Stella Maris College,
Chennai - 600 086
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
145
152
http://ijm2c.iauctb.ac.ir/article_663820_4b8b93046f903469c87dd367b69a6894.pdf
Solving Fuzzy Impulsive Fractional Differential Equations by Homotopy Perturbation Method
Nematallah
Najafi
Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, Iran
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
153
170
http://ijm2c.iauctb.ac.ir/article_663821_d4de011e5489a60d0f20ea7f06b1afc8.pdf
Steady-State and Dynamic Simulations of Gas Absorption Column Using MATLAB and SIMULINK
Naved
Siraj
Central Institute of Plastics Engineering and Technology, Bhopal
author
Abdul
Hakim
Department of Chemical Engineering
Aligarh Muslim University
Aligarh - India
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
171
188
http://ijm2c.iauctb.ac.ir/article_663822_2028ef09741eec47c845474c22332361.pdf
Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method
Ghasem
Kazemi Gelian
Department of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, Iran
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
189
198
http://ijm2c.iauctb.ac.ir/article_663823_efb31dc80cfcf1d7ffb1498932df68d6.pdf
Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation
M.
Karimian
Department mathematics payame noor university of tehran,Iran
author
A.
Karimian
Department of Mathematics, University of Tehran, Iran.
author
text
article
2018
eng
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.
International Journal of Mathematical Modelling & Computations
Islamic Azad University, Central tehran Branch
2228-6225
8
v.
3 (SUMMER)
no.
2018
199
206
http://ijm2c.iauctb.ac.ir/article_663825_5f143c09628fc5b1792b0614fab02b58.pdf