Computational Methods for Differential EquationsComputational Methods for Differential Equations
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Tue, 22 Jan 2019 06:46:27 +0100FeedCreatorComputational Methods for Differential Equations
http://cmde.tabrizu.ac.ir/
Feed provided by Computational Methods for Differential Equations. Click to visit.Finite integration method with RBFs for solving time-fractional convection-diffusion equation ...
http://cmde.tabrizu.ac.ir/article_8080_1088.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.Mon, 31 Dec 2018 20:30:00 +0100Nordsieck representation of high order predictor-corrector Obreshkov methods and their ...
http://cmde.tabrizu.ac.ir/article_8246_1088.html
Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method is discussed by providing Nordsieck representation of the method and preparing an starting procedure, an estimate for local truncation error and a formula for changing stepsize. Efficiency and capability of the method are shown by some numerical experiments.Mon, 31 Dec 2018 20:30:00 +0100The modified BFGS method with new secant relation for unconstrained optimization problems
http://cmde.tabrizu.ac.ir/article_8090_1088.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, 31 Dec 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_1088.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.Mon, 31 Dec 2018 20:30:00 +0100Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional ...
http://cmde.tabrizu.ac.ir/article_8082_1088.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.Mon, 31 Dec 2018 20:30:00 +0100An efficient improvement of the Newton method for solving nonconvex optimization problems
http://cmde.tabrizu.ac.ir/article_8078_1088.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.Mon, 31 Dec 2018 20:30:00 +0100Multi-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation
http://cmde.tabrizu.ac.ir/article_8233_1088.html
A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the soliton solutions are also found. Furthermore, three-dimensional plots of the wave solutions and its potential functions are given to visualize the dynamics of the model and their energy. We also provided the corresponding density plot of the solutions to understand the real direction and particles density in the waves which help to realize the elastic situations of the achieved solutions.Mon, 31 Dec 2018 20:30:00 +0100On the solving of matrix equation of Sylvester type
http://cmde.tabrizu.ac.ir/article_8308_1088.html
A solution of two problems related to the matrix equation of Sylvester type is given. In the first problem, the procedures for linear matrix inequalities are used to construct the solution of this equation. In the second problem, when a matrix is given which is not a solution of this equation, it is required to find such solution of the original equation, which most accurately approximates the given matrix. For this, an algorithm for constructing a general solution of the Sylvester matrix equation is used. The effectiveness of the proposed approaches is illustrated on the examples.Mon, 31 Dec 2018 20:30:00 +0100$L^p$-existence of mild solutions of fractional differential equations in Banach space
http://cmde.tabrizu.ac.ir/article_8250_1088.html
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. Mon, 31 Dec 2018 20:30:00 +0100Properties of utility function for Barles and Soner model
http://cmde.tabrizu.ac.ir/article_8178_1088.html
The nonlinear Black-Scholes equation has been increasingly attracting interest over the last two decades, because it provides more accurate values by considering transaction costs as a viable assumption. In this paper we review the fully nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price and then we prove two new theorems in this realistic model.Mon, 31 Dec 2018 20:30:00 +0100The numerical values of the nodal points for the Sturm-Liouville equation with one turning point
http://cmde.tabrizu.ac.ir/article_8319_1088.html
An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established and results have been illustrated in tables and graphics.Mon, 31 Dec 2018 20:30:00 +0100Stable Gaussian radial basis function method for solving Helmholtz equations
http://cmde.tabrizu.ac.ir/article_8177_1088.html
‎Radial basis functions (RBFs) are a powerful tool for approximating the solution of high-dimensional problems‎. ‎They are often referred to as a meshfree method and can be spectrally accurate‎. ‎In this paper, we analyze a new stable method for evaluating Gaussian radial basis function interpolants based on the eigenfunction expansion‎. ‎We develop our approach in two-dimensional spaces for solving Helmholtz equations‎. ‎In this paper, the eigenfunction expansions are rebuilt based on Chebyshev polynomials which are more suitable in numerical computations‎. ‎Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method for solving two-dimensional Helmholtz equations‎.Mon, 31 Dec 2018 20:30:00 +0100