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Oct 30, 2018Open    AccessArticle

Correlation of Brownian Motions and Its Impact on a Reinsurer’s Optimal Investment Strategy and Reinsured Proportion under Exponential Utility Maximization and Constant Elasticity of Variance Model

Silas A. Ihedioha
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

Solving Three Dimensional and Time Depending PDEs by Haar Wavelets Method

Abdeljalil Nachaoui, Ekhlass S. Al-Rawi, Ahmed F. Qasim
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

Construction of Solitary Wave Solutions and Rational Solutions for mKdV Equation with Initial Value Problem by Homotopy Perturbation Method

Zhongzhou Dong, Fen Wang
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

Stability and Regularization Method for Inverse Initial Value Problem of Biparabolic Equation

Hongwu Zhang, Xiaoju Zhang
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

Iterative Method Based on the Truncated Technique for Backward Heat Conduction Problem with Variable Coefficient

Hongwu Zhang, Xiaoju Zhang
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

Forced Oscillation of Neutral Impulsive Parabolic Partial Differential Equations with Continuous Distributed Deviating Arguments

Guangjie Liu, Chengyong Wang
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

Analysis on the Propagation of the Fiber-Optic Signals in the Perturbed Nonlinear Schrodinger Equation

Qianqian Xing, Jiuli Yin, Lixin Tian
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’ sensitivity...

Oct 31, 2014Open    AccessArticle

Magnetohydrodynamic Flow of Viscous Fluid over a Non-Linearly Stretching Sheet

Yohannes Yirga, Daniel Tesfay
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 resulting 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...