Jan 31, 2019Open AccessArticle
In this paper, we mainly study the existence and uniqueness of solutions and the asymptotic behavior of solutions for three-dimensional globally modified Bénard systems with delays under local Lipschitz conditions.
Oct 30, 2018Open AccessArticle
This work investigated a reinsurer’s optimal investment strategy and the pro-portion he accepted for reinsurance under proportional reinsurance and expo-nential utility preference in the cases where the Brownian motions were corre-lated and where they did not correlate. The reinsurer invested in a market in which the price process of the risky asset is governed by constant elasticity of variance (CEV) model. The required Hamilton-
May 24, 2018Open AccessArticle
Haar wavelets are applied for solution of three
dimensional partial differential equations (PDEs) or time depending two dimensional
PDEs. The proposed method is mathematically simple and fast. Two techniques are used in numerical solution, the first based on
2D-Haar wavelets and the second based on 3D-Haar wavelets and we compare them.
To demonstrate the efficiency of the method, two test prob
Feb 28, 2018Open AccessArticle
The mKdV equation with the
initial value problem is studied numerically by means of the homotopy
perturbation method. The analytical approximate solutions of the mKdV equation
are obtained. Choosing the form of the initial value, the single solitary wave,
two solitary waves and rational solutions are presented, some of which are
shown by the plots.
May 14, 2015Open AccessArticle
We consider an inverse initial value problem of the
biparabolic equation; this problem is ill-posed and the regularization methods
are needed to stabilize the numerical computations. This paper firstly
establishes a conditional stability of Holder type, then uses a modified
regularization method to overcome its ill-posedness and gives the convergence
estimate under an a-priori assumption
for the exact solution. Finally, a numerical example is presented to show that
this method works well.
Apr 27, 2015Open AccessArticle
We consider a backward heat conduction problem (BHCP) with variable
coefficient. This problem is severely ill-posed in the sense of Hadamard and
the regularization techniques are required to stabilize numerical computations.
We use an iterative method based on the truncated technique to treat it. Under
an a-priori and an a-posteriori stopping rule for the
iterative step number, the convergence estimates are established. Some numerical
results show that this method is stable and fea...
Dec 22, 2014Open AccessArticle
This paper investigated oscillatory properties of solutions for nonlinear
parabolic equations with impulsive effects under two different boundary
conditions. By using integral averaging method, variable substitution and
functional differential inequalities, we established several sufficient
conditions. At last, we provided two examples to illustrate the results.
Nov 14, 2014Open AccessArticle
Chaos appears in the whole process of fiber-optic signal propagation with
one external perturbation due to the absence of damping. Via adding a proper controller,
chaos cannot be suppressed when the controller’s strength is weak. With the increase
of the controller strength, the fiber-optic signal can stay in a stable state. However,
unstable phenomenon occurs in the propagation of the fiber-optic signal when
the strength exceeds a certain degree. Moreover, we discuss the parameters’
Oct 31, 2014Open AccessArticle
In this paper, the Magnetohydrodynamic (MHD) Flow of
Viscous Fluid over a Nonlinear Stretching Sheet is investigated numerically.
The partial differential equations governing the flow are reduced to a non
linear ordinary differential equations by using similarity transformations. The
transformed equations are numerically solved by an explicit finite difference
scheme known as the Keller Box Method. The velocity profiles are determined
and the effects of the magnetic parameter and non l...