Computational Methods for Differential EquationsComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Sat, 17 Nov 2018 15:27:52 +0100FeedCreatorComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Feed provided by Computational Methods for Differential Equations. Click to visit.A numerical approach for variable-order fractional unified chaotic systems with time-delay
http://cmde.tabrizu.ac.ir/article_7678_946.html
This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To illustrate the effectiveness of the proposed scheme, dynamical behaviors of the variable-order fractional unified chaotic systems with time-delay are investigated in the time domain.Sun, 30 Sep 2018 20:30:00 +0100A new reduced mathematical model to simulate the action potential in end plate of skeletal ...
http://cmde.tabrizu.ac.ir/article_8076_0.html
Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is more realistic. Studying qualitative behavior and propagation of action potential through a cell with this model is time consuming .In this paper we try to use properties of variables of this model to reduced dimension of this dynamical model. We study qualitative behavior of obtained model and illustrate that this new model treats like the original model.Fri, 26 Oct 2018 20:30:00 +0100Solving singular integral equations by using orthogonal polynomials
http://cmde.tabrizu.ac.ir/article_7703_946.html
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solution of singular integral equations. The efficiency of the method is illustrated through some examples.Sun, 30 Sep 2018 20:30:00 +0100An efficient improvement of the Newton method for solving nonconvex optimization problems
http://cmde.tabrizu.ac.ir/article_8078_0.html
‎Newton method is one of the most famous numerical methods among the line search‎ ‎methods to minimize functions. ‎It is well known that the search direction and step length play important roles ‎in this class of methods to solve optimization problems. ‎In this investigation‎, ‎a new modification of the Newton method to solve ‎unconstrained optimization problems is presented‎. ‎The significant merit of the proposed method is that ‎the step length $alpha_k$ at each iteration is equal to 1‎. ‎ Additionally, the convergence analysis for this iterative algorithm‎ ‎is established under suitable conditions‎. ‎Some illustrative examples are provided to show the validity and applicability of‎ ‎the presented method and a comparison is made with several other existing methods‎.Sun, 28 Oct 2018 20:30:00 +0100Space-time radial basis function collocation method for one-dimensional advection-diffusion problem
http://cmde.tabrizu.ac.ir/article_7670_946.html
The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validity of the presented method.Sun, 30 Sep 2018 20:30:00 +0100Finite integration method with RBFs for solving time-fractional convection-diffusion equation ...
http://cmde.tabrizu.ac.ir/article_8080_0.html
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integration by using initial condi-tions. This leads to fewer computations rather than the standard FIM. Also, a product Simpson method is used to overcome the singularity included in the definition of fractional derivatives, and an integration matrix is obtained. Some numerical examples are provided to show the efficiency of the method. In addition, a comparison is made between the proposed method and the previous ones.Fri, 02 Nov 2018 20:30:00 +0100An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic ...
http://cmde.tabrizu.ac.ir/article_7715_946.html
In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by Grau et al. in cite{Grau} to investigate when a collection of Abelian integrals is Chebyshev.Sun, 30 Sep 2018 20:30:00 +0100Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional ...
http://cmde.tabrizu.ac.ir/article_8082_0.html
‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry operators as a Lie algebra are clarified and the classification of subalgebras under adjoint transformation is given‎. ‎Hamiltonian equations including Hamiltonian symmetry are obtained‎. ‎Finally a modified virsion of Noether’s method including the direct method are applied in order to find local conservation laws of the equation‎.Sat, 03 Nov 2018 20:30:00 +0100Chebyshev finite difference method for solving a mathematical model arising in wastewater ...
http://cmde.tabrizu.ac.ir/article_7669_946.html
The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the problem to a set of algebraic equations. Numerical results are included to demonstrate the validity and applicability of the technique and a comparison is made with the existing results.Sun, 30 Sep 2018 20:30:00 +0100The modified BFGS method with new secant relation for unconstrained optimization problems
http://cmde.tabrizu.ac.ir/article_8090_0.html
Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. Under appropriate conditions, we show that the proposed method is globally convergent without needing convexity assumption on the objective function. Comparative results show computational effciency of the proposed method in the sense of the Dolan-More performance prolies.Mon, 05 Nov 2018 20:30:00 +0100A total variation diminishing high resolution scheme for nonlinear conservation laws
http://cmde.tabrizu.ac.ir/article_7677_946.html
In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total variation diminishing (TVD). The TVD schemes are robust against the spurious oscillations and preserve the sharpness of the solution near the sharp discontinuities and shocks. We also, prove the positivity and maximum-principle properties for this scheme. The numerical results are presented for both of the advection and Burger’s equation. A comparison of numerical results with some classical limiter functions is also provided.Sun, 30 Sep 2018 20:30:00 +0100A numerical technique for solving a class of 2D variational problems using Legendre spectral method
http://cmde.tabrizu.ac.ir/article_7648_946.html
An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage of the Ritz method is that it provides greater flexibility in which the boundary conditions are imposed at the end points of the interval. Furthermore, compared with the exact and eigenfunction solutions of the presented problems, the satisfactory results are obtained with low terms of basis elements. The convergence of the method is extensively discussed and finally two illustrative examples are included to demonstrate the validity and applicability of the proposed technique.Sun, 30 Sep 2018 20:30:00 +0100Rational Chebyshev Collocation approach in the solution of the axisymmetric stagnation flow on ...
http://cmde.tabrizu.ac.ir/article_7702_946.html
In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper similarity transformations. The approach is named the rational Chebyshev collocation (RCC) method. This method reduces this nonlinear ordinary differential equation to an algebraic equations system. RCC method is a strong kind of the collocation technique to solve the problems of boundary value over a semi-infinite interval without truncating them to a finite domain. We also present the comparison of this work with others and show that the present method is more effective and precise.Sun, 30 Sep 2018 20:30:00 +0100Homotopy perturbation method for eigenvalues of non-definite Sturm-Liouville problem
http://cmde.tabrizu.ac.ir/article_7708_946.html
In this paper, we consider the application of the homotopy perturbation method (HPM) to compute the eigenvalues of the Sturm-Liouville problem (SLP) which is called non-definite SLP. Two important Examples show that HPM is reliable method for computing the eigenvalues of SLP.Sun, 30 Sep 2018 20:30:00 +0100