2018-11-17T15:29:12Z
http://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=663
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
Mina
Mortazavi
Mohammad
Mirzazadeh
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by jacobi elliptic functions for the 1D MCGL equation are derived. Homogeneous method is a powerful method, it can be used to construct a large families of exact solutions to different nonlinear differential equations that does not involve independent variables.
Exact traveling wave Solutions
Modified Complex Ginzburg-Landau equation
$(G'/G)$-expanson method
Homogeneous balance method
Eextended F-expansion method
2015
04
01
70
86
http://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Optimization with the time-dependent Navier-Stokes equations as constraints
Mitra
Vizheh
Syaed Hodjatollah
Momeni-Masuleh
Alaeddin
Malek
In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.
Optimal Control Problems
Navier-Stokes equations
PDE-constrained optimization
quasi-Newton algorithm
Finite difference
2015
04
01
87
98
http://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Application of the block backward differential formula for numerical solution of Volterra integro-differential equations
Somayyeh
Fazeli
In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff VIDEs.
Volterra integro-differential equations
Block methods
Backward differential formula
2015
04
01
99
100
http://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Numerical solution of time-dependent foam drainage equation (FDE)
Murat
Gubes
Yildiray
Keskin
Galip
Oturanc
Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear partial differential equations (PDEs), it can be applied very easily and it has less computational work than other existing methods like Adomian decomposition and Laplace decomposition. Additionally, effectiveness and precision of RDTM solutions are shown in tables and graphically.
Foam Drainage Equation
Laplace Decomposition Method
Adomian Decomposition Method
Reduced Differential Transform Method
2015
04
01
111
122
http://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
Rahmat
Darzi
Bahram
Agheli
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
Boundary value problem
fixed point theorem
Partially ordered set
Positive solution
nondecreasing solution
2015
04
01
123
133
http://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2015
3
2
Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimension
Manjit
Singh
As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of associated linear problem or Lax pair are presented in straightforward manner and finally for proposed nonlinear equation, explicit one, two and three soliton solutions are also obtained.
Soliton solutions
Bilinear Backlund transformations
Lax pairs
Perturbation expansion
2015
04
01
134
146
http://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdf