University of TabrizComputational Methods for Differential Equations2345-39827320190701A numerical study using finite element method for generalized Rosenau-Kawahara-RLW equation3193339009ENSeydi BattalGazi KarakocDepartment of Mathematics, Faculty of Science and Art,
Nevsehir Haci Bektas Veli University, 50300 Nevsehir, TurkeySamirKumar BhowmikDepartment of Mathematics,
University of Dhaka, 1000 Dhaka, BangladeshFuzhengGaoSchool of Mathematics, Shandong University,
Shanda Nanlu 27, Jinan 250100, Shandong, P. R. ChinaJournal Article20180918In 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.https://cmde.tabrizu.ac.ir/article_9009_e78145fd7e6ec1e1f3ca8e75b6693211.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Analysis of the stability and convergence of a finite difference approximation for stochastic partial differential equations3343589008ENMehranNamjooDepartment of Mathematics, Vali-e-Asr University
of Rafsanjan, Rafsanjan, IranAliMohebbianDepartment of Mathematics, Vali-e-Asr University
of Rafsanjan, Rafsanjan, IranJournal Article20170611In 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.<br /> https://cmde.tabrizu.ac.ir/article_9008_ce59ca890bdc1d7c73670885e034a11d.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Application of the invariant subspace method in conjunction with the fractional Sumudu’s transform to a nonlinear conformable time-fractional dispersive equation of the fifth order3593699015ENKamyarHosseiniDepartment of Mathematics, Rasht Branch,
Islamic Azad University, Rasht, IranZainabAyatiDepartment of Engineering Sciences, Faculty of Technology and Engineering,
University of Guilan, East of Guilan, Rudsar, Iran0000-0001-5854-1051RezaAnsariDepartment of Mechanical Engineering, University of Guilan,
P. O. Box 3756, Rasht, IranJournal Article20180419During 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.https://cmde.tabrizu.ac.ir/article_9015_c0ff2d70963e581ac7c548fb1a9c965d.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Analytical approximate solution of leptospirosis epidemic model with standard incidence rate3703829033ENRukhsarIkramDepartment of Mathematics and Statistics,
University of Swat, Khyber Pakhtunkhwa, PakistanAmirKhanDepartment of Mathematics and Statistics,
University of Swat, Khyber Pakhtunkhwa, PakistanAsafKhanDepartment of Mathematics, University of Malakand,
Chakdara, Dir(Lower), Khyber Pakhtunkhwa, PakistanTahirKhanDepartment of Mathematics, University of Malakand,
Chakdara, Dir(Lower), Khyber Pakhtunkhwa, PakistanGulZamanDepartment of Mathematics, University of Malakand,
Chakdara, Dir(Lower), Khyber Pakhtunkhwa, PakistanJournal Article20180121In 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.https://cmde.tabrizu.ac.ir/article_9033_9709306950646a45662db9c1d8c154bc.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Unknown functions estimation in a parabolic equation arises from Diffusion Tensor Magnetic Resonance Imaging3833959010ENFahimehSoltanianDepartment of Mathematics, Payame Noor University,
P. O. Box 19395-3697, Tehran, Iran0000-0003-3068-3378MortezaGarshasbiDepartment of Mathematics, Iran University of Science
and Technology, P. O. Box 16846-13114, Tehran, IrannullJournal Article20180710In 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.https://cmde.tabrizu.ac.ir/article_9010_b8fa1ddb8daa253fb30ef6300dcfaf9e.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701A novel hybrid method for solving combined functional neutral differential equations with several delays and investigation of convergence rate via residual function3964179074ENOmur KıvancKurkcuDepartment of Mathematics,
Izmir University of Economics, Izmir 35330, Turkey0000-0002-3987-7171ErsinAslanDepartment of Software Engineering,
Manisa Celal Bayar University, Manisa 45400, TurkeyMehmetSezerDepartment of Mathematics,
Manisa Celal Bayar University, Manisa 45140, TurkeyJournal Article20180816In 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.https://cmde.tabrizu.ac.ir/article_9074_4ea5b510b8be8e937e9ad961a3372745.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Existence of bound states for non-local fourth-order Kirchhoff systems4184339032ENAlamehGhelichiDepartment of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, P. O. Box 47416-1468, Babolsar, IranMohsenAlimohammadyDepartment of Mathematics, Faculty of Basic Sciences,
University of Mazandaran, P. O. Box 47416-1468, Babolsar, IranJournal Article20180225This 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.https://cmde.tabrizu.ac.ir/article_9032_c2cea18cd3ee196ec661872713b5ef9f.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Application of cubic B-splines collocation method for solving nonlinear inverse diffusion problem4344539017ENHamedZeidabadiFaculty of Engineering, Sabzevar University
of New Technology, Sabzevar, IranRezaPourgholiSchool of Mathematics and Computer Science,
Damghan University, P. O. Box 36715-364, Damghan, IranSeyed HashemTabasiSchool of Mathematics and Computer Science,
Damghan University, P. O. Box 36715-364, Damghan, IranJournal Article20171104In this paper, we developed a collocation method based on cubic B-spline for solving nonlinear inverse parabolic partial differential equations as the following form<br /> \begin{align*}<br /> u_{t} &= [f(u)\,u_{x}]_{x} + \varphi(x,t,u,u_{x}),\,\quad\quad 0 < x < 1,\,\,\, 0 \leq t \leq T,<br /> \end{align*}<br /> 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.https://cmde.tabrizu.ac.ir/article_9017_03f4a26205c44ec1859b1a984f5fa3fa.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Dynamics of a predator-prey system with prey refuge4544749014ENZeynabLajmiriSama technical and vocational training college,
Izeh Branch, Islamic Azad University, Izeh, IranImanOrakSama technical and vocational training college,
Izeh Branch, Islamic Azad University, Izeh, IranSamaneHosseiniSama technical and vocational training college,
Izeh Branch, Islamic Azad University, Izeh, IranJournal Article20180223In 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.https://cmde.tabrizu.ac.ir/article_9014_f1e76cb4305792b7763e210ead9b349c.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Multiplicity of solutions for a p-Laplacian equation with nonlinear boundary conditions4754799007ENMohsenZivari-RezapourFaculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, IranMehdiJalalvandFaculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20180314In 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:<br /> <br /> \begin{eqnarray*}<br /> \left\{ \begin{array}{ll} \Delta_p u = a(x) |u|^{p-2} u & \mbox{ in<br /> $\Omega$,}\\\\ |\nabla u|^{p-2} \nabla u . \nu = \lambda f(x,u)<br /> & \mbox{ on $\partial\Omega$.}\end{array} \right.<br /> \end{eqnarray*}https://cmde.tabrizu.ac.ir/article_9007_1130136864015af834e427b0471877bb.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701On a novel modification of the Legendre collocation method for solving fractional diffusion equation4804969054ENHoseinJalebDepartment of Mathematics, Central Tehran Branch,
Islamic Azad University, Tehran, IranHojatollahAdibiDepartment of Applied Mathematics,
Faculty of Mathematics and Computer Science,
Amirkabir University Of Technology, Tehran, Iran0000-0002-8167-5020Journal Article20190120In 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.https://cmde.tabrizu.ac.ir/article_9054_78449bf314b7eaeac899c9f5ad8042dc.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39827320190701Cubic B-splines collocation method for solving a partial integro-differential equation with a weakly singular kernel4975109081ENMohammadGholamianDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, International Campus, Mashhad, IranJafarSaberi-NadjafiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, IranAli RezaSoheiliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, International Campus, Mashhad, IranJournal Article20170918In 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.https://cmde.tabrizu.ac.ir/article_9081_7c10be7531734646dcb54147fce3ec65.pdf