eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-01
1
1
1
15
231
A High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients
Javad Farzi
1
Sahand University Of Technology
This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditions. We derive the required linear systems for evaluation of the coefficients of such a nonstandard method. The given novel modeling provides an overall fifth order numerical model for two dimensional acoustic wave equation with discontinuous coefficients.
http://cmde.tabrizu.ac.ir/article_231_e22984f025d7dacb0d33f0f8384d3d84.pdf
Interface methods
two dimensional acoustic wave equation
high order methods
Lax-Wendroff method
WENO
discontinuous coefficients
Jump conditions
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-20
1
1
16
29
242
Chebyshev Spectral Collocation Method for Computing Numerical Solution of Telegraph Equation
M. Javidi
mo_javidi@yahoo.com
1
University of Tabriz
In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform telegraph equation to system of partial differential equations with initial condition. Using Chebyshev differentiation matrices yields a system of ordinary differential equations. Secondly, we apply fourth order Runge-Kutta formula for the numerical integration of the system of ODEs. Numerical results verified the high accuracy of the new method, and its competitive ability compared with other newly appeared methods.
http://cmde.tabrizu.ac.ir/article_242_25ad79d0795b8c4807a3d86288473135.pdf
Chebyshev spectral collocation method
telegraph equation
numerical results
Runge-Kutta formula
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-20
1
1
30
38
259
2-stage explicit total variation diminishing preserving Runge-Kutta methods
M. Mehdizadeh Khalsaraei
muhammad.mehdizadeh@gmail.com
1
F. Khodadosti
fayyaz64dr@gmail.com
2
University of Maragheh
University of Maragheh
In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities.
http://cmde.tabrizu.ac.ir/article_259_f275211af12c25479a94ac0787dc3e03.pdf
Initial value problem
Method of line
Total-variation-diminishing
Rung-Kutta methods
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-20
1
1
39
54
260
Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations
Kazem Ghanbari
1
Yousef Gholami
2
Sahand University of Technology
Sahand University of Technology
In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.
http://cmde.tabrizu.ac.ir/article_260_01737ac7f4a2458cfc9c83932cc6ebdb.pdf
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-20
1
1
55
70
277
Parameter determination in a parabolic inverse problem in general dimensions
Reza Zolfaghari
rzolfaghari@iust.ac.ir
1
Salman Farsi University of Kazerun
It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse problem to a Volterra integral equation of convolution-type. By using an explicit procedure based on Sinc function properties, the resulting integral equation is replaced by a system of linear algebraic equations. The convergence analysis is included, and it is shown that the error in the approximate solution is bounded in the infinity norm by the condition number and the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system. Some numerical examples are given to demonstrate the computational efficiency of the method.
http://cmde.tabrizu.ac.ir/article_277_64be06a89a3e7813e006630e885ee04c.pdf
eng
University of Tabriz
Computational Methods for Differential Equations
2345-3982
2383-2533
2013-12-20
1
1
71
77
306
The modified simplest equation method and its application
M. Akbari
1
University of Guilan
In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and can be used to solve other nonlinear partial differential equations in mathematical physics.
http://cmde.tabrizu.ac.ir/article_306_fcbed350396f3b4bf56c373881e123f7.pdf
The modified simplest equation method
traveling wave solutions
homogeneous balance
Solitary wave solutions
The generalized forms $B(n
1)$ and $B(-n
1)$ of Burgers equation