Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
High order immersed interface method for acoustic wave equation with discontinuous coeffcients
1
24
EN
J.
Farzi
0000-0001-9169-7920
Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran.
farzi@sut.ac.ir
S. M.
Hosseini
0000-0001-6841-497X
Department of Mathematics, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran.
hossei_m@modares.ac.ir
10.22067/ijnao.v4i1.26174
This paper concerns the numerical solution of the acoustic wave equation that contains interfaces in the solution domain. To solve the interface problems with high accuracy, more attention should be paid to the interfaces. In fact, any direct application of a high order finite diffierence method to these problems leads to inaccurate proximate solutions with high oscillations at the interfaces. There is however, the possibility of deriving some high order methods to resolve this phenomenon at the interfaces. In this paper, a sixth order immersed interface method for acoustic wave equation is presented. The order of accuracy is also maintained at the discontinuity using the jump conditions. Some numerical experiments are included which confirm the order of accuracy and numerical stability of the presented method.
Interface methods,High order methods,Lax-Wendroff method,Discontinuous coeffcients,Jump conditions
https://ijnao.um.ac.ir/article_24425.html
https://ijnao.um.ac.ir/article_24425_3ebf5fe9be4d7e6c05d025a0c1e91164.pdf
Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
Numerical solution of stiff systems of differential equations arising from chemical reactions
25
39
EN
G.
Hojjati
0000-0001-8406-763X
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
ghojjati@yahoo.com
A.
Abdi
0000-0002-0819-5557
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
a_abdi@tabrizu.ac.ir
F.
Mirzaee
Department of Mathematics, Faculty of Science, Malayer University, Malayer, Iran
f.mirzaee@malayeru.ac.ir
S.
Bimesl
Department of Mathematics, Faculty of Science, Malayer University, Malayer, Iran
saeed.math85@yahoo.com
10.22067/ijnao.v4i1.25339
Long time integration of large stiff systems of initial value problems, arising from chemical reactions, demands efficient methods with good accuracy and extensive absolute stability region. In this paper, we apply second derivative general linear methods to solve some stiff chemical problems such as chemical Akzo Nobel problem, HIRES problem and OREGO problem.
General linear methods,Ordinary differential equation,Chemical reactions,Stiff systems
https://ijnao.um.ac.ir/article_24426.html
https://ijnao.um.ac.ir/article_24426_cf8cec1ccb0c67a1bc7e12bb96d4847d.pdf
Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
A numerical technique based on operational matrices for solving nonlinear integro-differential equations
41
56
EN
A.
Golbabai
golbabai@iust.ac.ir
10.22067/ijnao.v4i1.34848
This paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order Volterra-Fredholm integro-differential equation(VFIDEs) and nonlinear fractional order integro-differential equations.<br /> Our tools for this aims is operational matrices of integration and fractional integration. By this method the given problems reduce to solve a system of algebraic equations. Illustrative examples are included to demonstrate the efficiency and high accuracy of the method.
Operational matrix of integration,Volterra-Fredholm,Nonlinear system of integro-differential equations,Fractional order,Legendre wavelet
https://ijnao.um.ac.ir/article_24427.html
https://ijnao.um.ac.ir/article_24427_007c80186efb4e34f348d98ab56f26bf.pdf
Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
Solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space
57
76
EN
M.
Mohammadi
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.
m_mohammadi@math.iut.ac.ir
R.
Mokhtari
0000-0002-1420-0949
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.
mokhtari@cc.iut.ac.ir
F. T.
Isfahani
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-
83111, Iran.
f_toutianisfahani@math.iut.ac.ir
10.22067/ijnao.v4i1.23266
On the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. The convergence of vn to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such inverse problems.
Inverse Problem,Parabolic equation,Nonlocal boundary conditions,Reproducing kernel space
https://ijnao.um.ac.ir/article_24428.html
https://ijnao.um.ac.ir/article_24428_71b4a0f6a2a54c4d163f95a93e30769f.pdf
Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
An approximation method for numerical solution of multi-dimensional feedback delay fractional optimal control problems by Bernstein polynomials
77
94
EN
E.
Safaie
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi university of Mashhad, Mashhad, Iran.
elahesafaie_62@yahoo.com
M. H.
Farahi
0000-0002-9711-6936
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi university of Mashhad, Mashhad, Iran, and The center of Excellence on Modelling and Control Systems (CEMCS), Mashhad, Iran.
farahi@math.um.ac.ir
10.22067/ijnao.v4i1.28711
In this paper we present a new method for solving fractional optimal control problems with delays in state and control. This method is based upon Bernstein polynomial basis and using feedback control. The main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. In this work, we use Bernstein polynomials to transform the fractional time-varying multi-dimensional optimal control system with both state and control delays, into an algabric system in terms of the Bernstein coefficients approximating state and control functions. We use Caputo derivative of degree 0 < a ≤ 1 as the fractional derivative in our work. Finally, some numerical examples are given to illustrate the effectiveness of this method.
Delay fractional optimal control problem,Caputo fractional derivative,Bernstein polynomial
https://ijnao.um.ac.ir/article_24429.html
https://ijnao.um.ac.ir/article_24429_c65817d47dbd9743232148d1fd0c944f.pdf
Ferdowsi University of Mashhad
Iranian Journal of Numerical Analysis and Optimization
2423-6977
2423-6969
4
1
2014
05
01
A successive iterative approach for two dimensional nonlinear Volterra-Fredholm integral equations
95
104
EN
A. H.
Borzabadi
School of Mathematics and Computer Science, Damghan University, Damghan, Iran.
borzabadi@mazust.ac.ir
M.
Heidari
School of Mathematics and Computer Science, Damghan University, Damghan, Iran.
hedari@yahoo.com
10.22067/ijnao.v4i1.34849
In this paper, an iterative scheme for extracting approximate solutions of two dimensional Volterra-Fredholm integral equations is proposed. Considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. Several examples are provided to demonstrate the effciency of the approach.
Volterra-Fredholm integral equation,Iterative method,Dis- cretization,Approximation
https://ijnao.um.ac.ir/article_24430.html
https://ijnao.um.ac.ir/article_24430_2ada4dabb216b3e8c7ab32a9284857d4.pdf