2024-03-28T23:23:13Z
https://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=1136
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
A numerical study using finite element method for generalized Rosenau-Kawahara-RLW equation
Seydi Battal
Gazi Karakoc
Samir
Kumar Bhowmik
Fuzheng
Gao
In this paper, we are going to obtain the soliton solution of the generalized Rosenau-Kawahara-RLW equation that describes the dynamics of shallow water waves in oceans and rivers. We confirm that our new algorithm is energy-reserved and unconditionally stable. In order to determine the performance of our numerical algorithm, we have computed the error norms $L_{2}$ and $L_{\infty }$. Convergence of full discrete scheme is firstly studied. Numerical experiments are implemented to validate the energy conservation and effectiveness for longtime simulation. The obtained numerical results have been compared with a study in the literature for similar parameters. This comparison clearly shows that our results are much better than the other results.
Generalized Rosenau-Kawahara-RLW equation
finite element method
Collocation
2019
07
01
319
333
https://cmde.tabrizu.ac.ir/article_9009_e78145fd7e6ec1e1f3ca8e75b6693211.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Analysis of the stability and convergence of a finite difference approximation for stochastic partial differential equations
Mehran
Namjoo
Ali
Mohebbian
In this paper, an implicit finite difference scheme is proposed for the numerical solution of stochastic partial differential equations (SPDEs) of Ito type. The consistency, stability and convergence of the scheme is analyzed. Numerical experiments are included to show the efficiency of the scheme.
Stochastic partial differential equations
Stochastic finite difference scheme
Stability
Consistency
Convergence
2019
07
01
334
358
https://cmde.tabrizu.ac.ir/article_9008_ce59ca890bdc1d7c73670885e034a11d.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Application of the invariant subspace method in conjunction with the fractional Sumudu’s transform to a nonlinear conformable time-fractional dispersive equation of the fifth order
Kamyar
Hosseini
Zainab
Ayati
Reza
Ansari
During the past years, a wide range of distinct approaches has been exerted to solve the nonlinear fractional differential equations (NLFDEs). In this paper, the invariant subspace method (ISM) in conjunction with the fractional Sumudu’s transform (FST) in the conformable context is formally adopted to deal with a nonlinear conformable time-fractional dispersive equation of the fifth order. As an outcome, a new exact solution of the model is procured, corroborating the exceptional performance of the hybrid scheme.
Fifth order time-fractional dispersive equation
Conformable context
Invariant subspace method
Fractional Sumudu’s transform
A new exact solution
2019
07
01
359
369
https://cmde.tabrizu.ac.ir/article_9015_c0ff2d70963e581ac7c548fb1a9c965d.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Analytical approximate solution of leptospirosis epidemic model with standard incidence rate
Rukhsar
Ikram
Amir
Khan
Asaf
Khan
Tahir
Khan
Gul
Zaman
In this paper, we consider a mathematical model of leptospirosis disease which is an infectious disease. The model we are considering is a system of nonlinear ordinary differential equations and it is difficult to find exact solution. In order to compute the approximate solution, He's homotopy perturbation method is used. The findings obtained by HPM and Runge-Kutta fourth order (RK4) methods are compared. To show the simplicity and reliability of the method, sample plots are given at the end of the paper.
Leptospirosis
Homotopy perturbation method
Epidemic model
Numerical simulations
2019
07
01
370
382
https://cmde.tabrizu.ac.ir/article_9033_9709306950646a45662db9c1d8c154bc.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Unknown functions estimation in a parabolic equation arises from Diffusion Tensor Magnetic Resonance Imaging
Fahimeh
Soltanian
Morteza
Garshasbi
In this work, a general mathematical model of Diffusion Tensor Magnetic Resonance Imaging is formulated as an inverse problem. An effective numerical approach based on space marching method and mollifcation scheme is established to solve this problem. Convergence and stability of proposed approach are established. Using two test problems, the robustness and ability of the numerical approach is investigated.
Inverse problem
Magnetic Resonance Imaging
Mollification
Regularized problem marching approach
2019
07
01
383
395
https://cmde.tabrizu.ac.ir/article_9010_b8fa1ddb8daa253fb30ef6300dcfaf9e.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
A novel hybrid method for solving combined functional neutral differential equations with several delays and investigation of convergence rate via residual function
Omur Kıvanc
Kurkcu
Ersin
Aslan
Mehmet
Sezer
In this study, we introduce a novel hybrid method based on a simple graph along with operational matrix to solve the combined functional neutral differential equations with several delays. The matrix relations of the matching polynomials of complete and path graphs are employed in the matrix-collocation method. We improve the obtained solutions via an error analysis technique. The oscillation of them on time interval is also estimated by coupling the method with Laplace-Pad\'{e} technique. We develop a general computer program and so we can efficiently monitor the precision of the method. We investigate a convergence rate of the method by constructing a formula based on the residual function. Eventually, an algorithm is described to show the easiness of the method.
Collocation points
Graph theory
Laplace-Padé method
Matching polynomial
Vulnerability
2019
07
01
396
417
https://cmde.tabrizu.ac.ir/article_9074_4ea5b510b8be8e937e9ad961a3372745.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Existence of bound states for non-local fourth-order Kirchhoff systems
Alameh
Ghelichi
Mohsen
Alimohammady
This paper is concerned with existence of three solutions for non-local fourth-order Kirchhoff systems with Navier boundary conditions. Our technical approach is based on variational methods and the theory of the variable exponent Sobolev spaces.
Navier condition
(p(x)
q(x))-biharmonic systems
Variational method
Three critical points theorem
Variable exponent Sobolev spaces
2019
07
01
418
433
https://cmde.tabrizu.ac.ir/article_9032_c2cea18cd3ee196ec661872713b5ef9f.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Application of cubic B-splines collocation method for solving nonlinear inverse diffusion problem
Hamed
Zeidabadi
Reza
Pourgholi
Seyed Hashem
Tabasi
In this paper, we developed a collocation method based on cubic B-spline for solving nonlinear inverse parabolic partial differential equations as the following form \begin{align*} u_{t} &= [f(u)\,u_{x}]_{x} + \varphi(x,t,u,u_{x}),\,\quad\quad 0 < x < 1,\,\,\, 0 \leq t \leq T, \end{align*} where $f(u)$ and $\varphi$ are smooth functions defined on $\mathbb{R}$. First, we obtained a time discrete scheme by approximating the first-order time derivative via forward finite difference formula, then we used cubic B-spline collocation method to approximate the spatial derivatives and Tikhonov regularization method for solving produced ill-posed system. It is proved that the proposed method has the order of convergence $O(k+h^2)$. The accuracy of the proposed method is demonstrated by applying it on three test problems. Figures and comparisons have been presented for clarity. The aim of this paper is to show that the collocation method based on cubic B-spline is also suitable for the treatment of the nonlinear inverse parabolic partial differential equations.
Cubic B-spline
Collocation method
Inverse problems
Convergence analysis
Stability of solution
Tikhonov regularization method
Ill-posed problems
Noisy data
2019
07
01
434
453
https://cmde.tabrizu.ac.ir/article_9017_03f4a26205c44ec1859b1a984f5fa3fa.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Dynamics of a predator-prey system with prey refuge
Zeynab
Lajmiri
Iman
Orak
Samane
Hosseini
In this paper, we investigate the dynamical complexities of a prey predator model prey refuge providing additional food to predator. We determine dynamical behaviours of the equilibria of this system and characterize codimension 1 and codimension 2 bifurcations of the system analytically. Hopf bifurcation conditions are derived analytically. We especially approximate a family of limit cycles emanating from a Hopf point. The analytical results are in well agreement with the numerical simulation results. Our bifurcation analysis indicates that the system exhibits numerous types of bifurcation phenomena, including Hopf, and Bogdanov-Takens bifurcations.
Hopf Bifurcation
Bogdanov-Takens bifurcation
Dynamical behavior
Limit cycles
2019
07
01
454
474
https://cmde.tabrizu.ac.ir/article_9014_f1e76cb4305792b7763e210ead9b349c.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Multiplicity of solutions for a p-Laplacian equation with nonlinear boundary conditions
Mohsen
Zivari-Rezapour
Mehdi
Jalalvand
In this paper we use the three critical points theorem attributed to B. Ricceri in order to establish existence of three distinct solutions for the following boundary value problem: \begin{eqnarray*} \left\{ \begin{array}{ll} \Delta_p u = a(x) |u|^{p-2} u & \mbox{ in $\Omega$,}\\\\ |\nabla u|^{p-2} \nabla u . \nu = \lambda f(x,u) & \mbox{ on $\partial\Omega$.}\end{array} \right. \end{eqnarray*}
Three critical points
p-Laplacian
Multiplicity
existence
2019
07
01
475
479
https://cmde.tabrizu.ac.ir/article_9007_1130136864015af834e427b0471877bb.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
On a novel modification of the Legendre collocation method for solving fractional diffusion equation
Hosein
Jaleb
Hojatollah
Adibi
In this paper, a modification of the Legendre collocation method is used for solving the space fractional differential equations. The fractional derivative is considered in the Caputo sense along with the finite difference and Legendre collocation schemes. The numerical results obtained by this method have been compared with other methods. The results show the capability and efficiency of the proposed method.
Fractional diffusion equation
Caputo derivative
Fractional Riccati differential equation
Finite difference
Collocation
Legendre polynomials
2019
07
01
480
496
https://cmde.tabrizu.ac.ir/article_9054_78449bf314b7eaeac899c9f5ad8042dc.pdf
Computational Methods for Differential Equations
Comput. Methods Differ. Equ.
2345-3982
2345-3982
2019
7
3
Cubic B-splines collocation method for solving a partial integro-differential equation with a weakly singular kernel
Mohammad
Gholamian
Jafar
Saberi-Nadjafi
Ali Reza
Soheili
In this paper, we apply a numerical scheme for the solution of a second order partial integro-differential equation with a weakly singular kernel. In the time direction, the backward Euler method time-stepping is used to approximate the differential term and the cubic B-splines is applied to the space discretization. Detailed discrete schemes, the convergence and the stability of the method is demonstrated. Next, the computational efficiency and accuracy of the method are examined by the numerical results.
Cubic B-splines
Partial integro-differential equation
Backward Euler method
2019
07
01
497
510
https://cmde.tabrizu.ac.ir/article_9081_7c10be7531734646dcb54147fce3ec65.pdf