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An Hermitian Boundary Integral Hybrid Formulation for Nonlinear Fisher-Type Equations
Issue:
Volume 4, Issue 3, June 2015
Pages:
83-99
Received:
20 March 2015
Accepted:
29 March 2015
Published:
18 April 2015
Abstract: This paper explores the application of an Hermitian hybrid boundary integral formulation for handling Fisher-type equations. The Hermite system incorporates the problem unknowns with their space derivatives and as a consequence produces a relatively larger coefficient matrix than the corresponding linear approximation. However by adopting a finite element-like integral numerical procedure, the modified boundary integral formulation otherwise known as the Green element method (GEM) produces slender and sparse coefficient matrices which enhance an efficient solution algorithm. The resulting equations appear in the form of local elemental integral equations whose contributions add up to the coefficient matrix. This process is amply simplified in the Green element method due to the presence of the source point inside an element thereby encouraging integration to be carried out locally and accurately. This so called ‘divide and conquer’ approach is significantly much better than working with the entire matrix especially for nonlinear problems where an encounter with the problem domain can not be totally avoided. Numerical tests are carried out to illustrate the utility of this technique by comparing results obtained from both the Hermite and non-Hermite discretizations. It is observed that for each of the problems tested, not only do the results agree with those from literature, it took the Hermitian approximation fewer number of elements to achieve the same level of accuracy than its non-Hermitian version. However, application of same technique to multi-dimensional problems may not be as straightforward due to the construction and storing of the Hermite system matrix which will not only involve non-trivial operations in terms of a high computational cost but also a compromise in the quality of the numerical solution arising from significant round-off errors.
Abstract: This paper explores the application of an Hermitian hybrid boundary integral formulation for handling Fisher-type equations. The Hermite system incorporates the problem unknowns with their space derivatives and as a consequence produces a relatively larger coefficient matrix than the corresponding linear approximation. However by adopting a finite ...
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Second Law Analysis of Buoyancy Driven Unsteady Channel Flow of Nanofluids with Convective Cooling
Michael Hamza Mkwizu,
Oluwole Daniel Makinde,
Yaw Nkansah-Gyekye
Issue:
Volume 4, Issue 3, June 2015
Pages:
100-115
Received:
30 March 2015
Accepted:
12 April 2015
Published:
21 April 2015
Abstract: We investigate the combined effects of buoyancy force and convective cooling on entropy generation in unsteady channel flow of water based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both first and second laws of thermodynamics are utilised to analyze the model problem. Using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme, the governing partial differential equations are solved numerically. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed.
Abstract: We investigate the combined effects of buoyancy force and convective cooling on entropy generation in unsteady channel flow of water based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both first and second laws of thermodynamics are utilised to analyze the model problem. Using a semi discretization finite difference metho...
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Study on Dynamic Risk Measurement Based on ARMA-GJR-AL Model
Hong Zhang,
Li Zhou,
Jian Guo
Issue:
Volume 4, Issue 3, June 2015
Pages:
116-121
Received:
30 March 2015
Accepted:
16 April 2015
Published:
27 April 2015
Abstract: This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given of the Shanghai stock market and the New York stock market. And we study the effectiveness of the model. The results show that the dynamic risk measurement model based on AL distribution is more reasonable and applicability, so it can effectively measure risk.
Abstract: This paper established the ARMA-GJR-AL model of dynamic risk VaR and CVaR measurement. Considering from aspects of the correlation and volatility and residual distribution characteristics, studying the dynamic risk measures of VaR and CVaR based on ARMA-GJR-AL model. Through empirical research, Risk prediction and accuracy of inspection are given o...
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Exact and Solitary Wave Solutions to the Generalized Fifth-order KdV Equation by Using the Modified Simple Equation Method
M. Ashrafuzzaman Khan,
M. Ali Akbar
Issue:
Volume 4, Issue 3, June 2015
Pages:
122-129
Received:
10 April 2015
Accepted:
21 April 2015
Published:
30 April 2015
Abstract: Although the modified simple equation (MSE) method effectively provides exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the field of engineering and mathematical physics, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this article, we have exposed a process how to implement the MSE method to solve NLEEs for balance number two. In order to verify the process, the generalized fifth-order KdV equation has been solved. By means of this scheme, we found some fresh traveling wave solutions to the above mentioned equation. When the parameters receive special values, solitary wave solutions are derived from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process.
Abstract: Although the modified simple equation (MSE) method effectively provides exact traveling wave solutions to nonlinear evolution equations (NLEEs) in the field of engineering and mathematical physics, it has some limitations. When the balance number is greater than one, usually the method does not give any solution. In this article, we have exposed a ...
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Empirical Analysis of the Fractal Features Analysis on London Gold Futures Market
Hong Zhang,
Li Zhou,
Jian Guo
Issue:
Volume 4, Issue 3, June 2015
Pages:
130-134
Received:
5 April 2015
Accepted:
14 April 2015
Published:
4 May 2015
Abstract: In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original time series observation sequence. The result of R/S analysis shows that the movement of market prices of the financial markets has obvious nonperiodic circle, with Hurst index large than 0.5 and C (t) large than 0, which indicates clear fractal properties. And the result also shows that the influence of price limit on the fractal properties of London Gold Futures Market is very remarkable.
Abstract: In this paper, we study the fractal characteristics of the futures market. We take the empirical study on London Gold Futures yield by Rescaled Range Analysis, analyzing the fractal characteristics of the futures market. We further determine fractal characteristics and the structure of the nonlinear time series through random disturb the original t...
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Hydrogen-Natural Gas Mixture Leak Detection Using Reduced Order Modelling
Norazlina Subani,
Norsarahaida Amin,
Baba Galadima Agaie
Issue:
Volume 4, Issue 3, June 2015
Pages:
135-144
Received:
20 April 2015
Accepted:
6 May 2015
Published:
16 May 2015
Abstract: Transient pressure wave detection analysis to detect the location of leakage on a pipeline containinghydrogen-natural gas mixture is presented. The transient pressure wave is generated either by rapid or sudden closure of the downstream shut-off valve. The governing equations of unsteady, compressible and isothermal one-dimensional flow are solved using the reduced order modelling technique. The solutions obtained when the transient condition is generated using the rapid closure valve show good agreement with published results. When the sudden closure valve is considered, the transient pressure, celerity wave, mass flux and the amount of leak discharge are shown to increase when the hydrogen mass ratio is increased. The amount of leak discharge which is calculated based on the computed celerity and pressure waves is found to be dependent on the leak positions.
Abstract: Transient pressure wave detection analysis to detect the location of leakage on a pipeline containinghydrogen-natural gas mixture is presented. The transient pressure wave is generated either by rapid or sudden closure of the downstream shut-off valve. The governing equations of unsteady, compressible and isothermal one-dimensional flow are solved ...
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Meshless Local Petrov-Galerkin Method for Scattering from 2-D Rectangular Cavities in a Ground Plane
Issue:
Volume 4, Issue 3, June 2015
Pages:
145-151
Received:
2 April 2015
Accepted:
29 April 2015
Published:
23 May 2015
Abstract: In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no elements or background cells are needed, in either the interpolation or integration. Based on local weak form and the moving least square (MLS) approximation, this truly meshless method is applied to solve the scattering problem. The results of numerical experiments have shown the efficiency and accuracy of the proposed method.
Abstract: In this paper, we develop the meshless local Petrov-Galerkin formulation of the scattering from rectangular cavities embedded in a ground plane. The electromagnetic scattering by the cavity is governed by the Helmholtz equation along with Sommerfeld's radiation conditions imposed at infinity. The MLPG method is a truly meshless method wherein no el...
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Volterra Integral Equations with Vanishing Delay
Xiaoxuan Li,
Weishan Zheng,
Jiena Wu
Issue:
Volume 4, Issue 3, June 2015
Pages:
152-161
Received:
29 March 2015
Accepted:
6 May 2015
Published:
27 May 2015
Abstract: In this article, we use a Chebyshev spectral-collocation method to solve the Volterra integral equations with vanishing delay. Then a rigorous error analysis provided by the proposed method shows that the numerical error decay exponentially in the infinity norm and in the Chebyshev weighted Hilbert space norm. Numerical results are presented, which confirm the theoretical predicition of the exponential rate of convergence.
Abstract: In this article, we use a Chebyshev spectral-collocation method to solve the Volterra integral equations with vanishing delay. Then a rigorous error analysis provided by the proposed method shows that the numerical error decay exponentially in the infinity norm and in the Chebyshev weighted Hilbert space norm. Numerical results are presented, which...
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Taylor-SPH Method for Viscoplastic Damage Material
Hajar Idder,
Mokhtar Mabssout
Issue:
Volume 4, Issue 3, June 2015
Pages:
162-173
Received:
8 May 2015
Accepted:
17 May 2015
Published:
29 May 2015
Abstract: In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the method as a function of the smoothing length and the Courant number is analysed in the elastic case. The Taylor-SPH method is used to simulate localization in a one dimensional viscoplastic damage problem. The numerical results show that the Taylor-SPH method is able to model localization phenomena in viscoplastic damage material without lose of hyperbolicity of partial differential equations.
Abstract: In this paper, we apply the meshless method Taylor-SPH to solve the propagation of shock wave in viscoplastic material coupled to damage. The equations are written in terms of stress and velocity. Taylor-SPH method is based on the Taylor series expansion of stress and velocity and on the corrected SPH approximation. Numerical stability of the metho...
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Option Pricing Variance Reduction Techniques Under the Levy Process
Li Zhou,
Hong Zhang,
Jian Guo,
Shucong Ming
Issue:
Volume 4, Issue 3, June 2015
Pages:
174-180
Received:
8 May 2015
Accepted:
20 May 2015
Published:
29 May 2015
Abstract: After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.
Abstract: After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this c...
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Modelling Infectiology and Optimal Control of Dengue Epidemic
Laurencia Ndelamo Massawe,
Estomih S. Massawe,
Oluwole Daniel Makinde
Issue:
Volume 4, Issue 3, June 2015
Pages:
181-191
Received:
12 May 2015
Accepted:
22 May 2015
Published:
3 June 2015
Abstract: A mathematical model is presented to examine the interaction between human and vector populations. The model consists of five control strategies i.e. campaign aimed in educating careless individuals as a mean of minimizing or eliminating mosquito-human contact, control effort aimed at reducing mosquito-human contact, the control effort for removing vector breeding places, insecticide application and the control effort aimed at reducing the maturation rate from larvae to adult in order to reduce the number of infected individual. Optimal Control (OC) approach is used in order to find the best strategy to fight the disease and minimize the cost.
Abstract: A mathematical model is presented to examine the interaction between human and vector populations. The model consists of five control strategies i.e. campaign aimed in educating careless individuals as a mean of minimizing or eliminating mosquito-human contact, control effort aimed at reducing mosquito-human contact, the control effort for removing...
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Modelling Infectiology of Dengue Epidemic
Laurencia Ndelamo Massawe,
Estomih S. Massawe,
Oluwole Daniel Makinde
Issue:
Volume 4, Issue 3, June 2015
Pages:
192-206
Received:
13 May 2015
Accepted:
26 May 2015
Published:
8 June 2015
Abstract: In this paper a mathematical model for the transmission dynamics of dengue fever disease is presented. We present a SITR (susceptible, infected, treated, recovery) and ASI (aquatic, susceptible, infected) epidemic model to describe the interaction between human and dengue fever mosquito populations. In order to assess the transmission of Dengue fever disease, the susceptible population is divided into two, namely, careful and careless human susceptible population. The model presents four possible equilibria: two disease-free and two endemic equilibrium.The results show that the disease-free equilibrium point is locally and globally asymptotically stable if the reproduction number is less than unity. Endemic equilibrium point is locally and globally asymptotically stable under certain conditions using additive compound matrix and Lyapunov method respectively. Sensitivity analysis of the model is implemented in order to investigate the sensitivity of certain key parameters of dengue fever disease with treatment, Careful and Careless Susceptibles on the transmission of Dengue fever Disease.
Abstract: In this paper a mathematical model for the transmission dynamics of dengue fever disease is presented. We present a SITR (susceptible, infected, treated, recovery) and ASI (aquatic, susceptible, infected) epidemic model to describe the interaction between human and dengue fever mosquito populations. In order to assess the transmission of Dengue fev...
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Some Convalescent Methods for the Solution of Systems of Linear Equations
Issue:
Volume 4, Issue 3, June 2015
Pages:
207-213
Received:
16 May 2015
Accepted:
26 May 2015
Published:
9 June 2015
Abstract: In a variety of problems in the fields of physical sciences, engineering, economics, etc., we are led to systems of linear equations, Ax = b, comprising n linear equations in n unknowns x1, x2, …, xn, where A = [aij] is an nxn coefficient matrix, and x = [x1 x2 . . .xn]T, b = [b1 b2 . . .bn]T are the column vectors. There are many analytical as well as numerical methods[1}– [11] to solve such systems of equations, including Gauss elimination method, and its modifications namely Doolittle’s method, Crout’s method and Cholesky’s method, which employ LU-decomposition method, where L = [iij] and u = [uij] are the lower and upper triangular matrices respectively. The LU-decomposition method was first introduced by the mathematician Alan M. Turing[2]-[11] in 1948. Here, in this paper we have made an effort to modify the existing LU-decomposition methods to solve the above mentioned system Ax = b, with the least possible endeavour. It may be seen that the Gauss elimination method[1], [2], [3], [4] needs about 2n3/3 operations, while Doolittle’s and Crout’s methods require n2 operations. Accordingly, in these methods we are required to evaluate n2 number of unknown elements of the L and U matrices. Moreover, Cholesky’s method[1] requires 2n2/3 operations. Accordingly this method requires evaluation of 2n2/3 number of unknown elements of the L and U matrices But, in contrast, the improved Doolittle’s, Crout’s and Cholesky’s methods presented in this paper require evaluation of only (n–1)2 number of unknown elements of the L and U matrices. Moreover, an innovative method is also presented in this paper which requires evaluation of even less number of unknown elements of the L and U matrices. In this method we need to evaluate only (n–2)2 number of the said unknown elements. Thus, by employing these methods, the computational time and effort required for the purpose can substantially be reduced.
Abstract: In a variety of problems in the fields of physical sciences, engineering, economics, etc., we are led to systems of linear equations, Ax = b, comprising n linear equations in n unknowns x1, x2, …, xn, where A = [aij] is an nxn coefficient matrix, and x = [x1 x2 . . .xn]T, b = [b1 b2 . . .bn]T are the column vectors. There are many analytical as wel...
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Hedging Stock Options Using Futures Contracts on the Stock
Mihai Grigore Bunea Domsa
Issue:
Volume 4, Issue 3, June 2015
Pages:
214-219
Received:
8 May 2015
Accepted:
20 May 2015
Published:
16 June 2015
Abstract: The aim of this paper is to present the price and replicating strategy for an European option on spot (or cash) underlier with continuous dividend yield, when the instrument used in the dynamic hedging of the option is a futures contract on the respective underlier. It formalizes the heuristic practice among option traders to replicate options on a stock index using futures on the respective stock index and investigates weather the obtained results differ significantly from what they would get using the actual stock index, as required by Black-Scholes pricing. Heuristically, the substitution is supported by index and futures prices being close, at least for small dividends and time to maturity. Our method is to express this practice in accounting terms, derive the self-financing portfolio dynamics and then the closed form option price and delta. Finally, run numerical simulations and compare results obtained by Black-Scholes versus our approach. Results show both the price and delta formulas differ from Black-Scholes, however numeric simulation doesn’t yield high enough differences to warrant obvious arbitrage, meaning that while not rigorously exact, the approximation is good enough for most practical use cases.
Abstract: The aim of this paper is to present the price and replicating strategy for an European option on spot (or cash) underlier with continuous dividend yield, when the instrument used in the dynamic hedging of the option is a futures contract on the respective underlier. It formalizes the heuristic practice among option traders to replicate options on a...
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Ill-Posed Algebraic Systems with Noise Data
Vladimir V. Ternovski,
Mikhail M. Khapaev,
Alexander S. Grushicin
Issue:
Volume 4, Issue 3, June 2015
Pages:
220-224
Received:
31 May 2015
Accepted:
6 June 2015
Published:
19 June 2015
Abstract: Finding a numerical solution of linear algebraic equations is known to present an ill-posed in the sense that small perturbation in the right hand side may lead to large errors in the solution. It is important to verify the accuracy of an approximate solution by taking into account all possible errors in the elements of the matrix, and of the vector at the right hand side as well as roundoff errors. There may be computational difficulties with ill-posed systems as well. If to apply standard methods such as the method of Gauss elimination to such systems it may be not possible to obtain the correct solution though discrepancy can be less accuracy of data errors. Besides, a small discrepancy will not always guarantee proximity to a correct solution. Actually there is no need for preliminary assessment whether a given system of linear algebraic equations is inherently ill-conditioned or well-conditioned. In this paper we consider a new approach to the solution of algebraic systems, which is based on statistical effect in matrices of big order. It will be shown that the conditionality of the systems of equation may change with a high probability, if the matrix distorted by random noise. After applying some standard methods, we may introduce the received "chaotic" solution is used as a source of a priori information a more general variational problem.
Abstract: Finding a numerical solution of linear algebraic equations is known to present an ill-posed in the sense that small perturbation in the right hand side may lead to large errors in the solution. It is important to verify the accuracy of an approximate solution by taking into account all possible errors in the elements of the matrix, and of the vecto...
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