Search results for: (2 1)-dimensional breaking soliton equation
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1160

Search results for: (2 1)-dimensional breaking soliton equation

1070 On the Existence and Global Attractivity of Solutions of a Functional Integral Equation

Authors: Asadollah Aghajani, Yaghoub Jalilian

Abstract:

Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.

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1069 Assessment of Hargreaves Equation for Estimating Monthly Reference Evapotranspiration in the South of Iran

Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

Abstract:

Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.

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1068 On CR-Structure and F-Structure Satisfying Polynomial Equation

Authors: Manisha Kankarej

Abstract:

The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, Integrability condition & Nijenhuis tensor.

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1067 Flowering Response of a Red Pitaya Germplasm Collection to Lighting Addition

Authors: Dinh-Ha Tran, Chung-Ruey Yen, Yu-Kuang H. Chen

Abstract:

A collection of thirty cultivars/clones of a red pitaya was used to investigate flowering response to lighting supplementation in the winter season of 2013-2014 in southern Taiwan. The night-breaking treatment was conducted during the period of 10 Oct. 2013 to 5 Mar. 2014 with 4-continuous hours (22.00 – 02.00 hrs) of additional lighting daily using incandescent bulbs (100W). Among cultivars and clones tested, twenty-three genotypes, most belonging to the red-magenta flesh type, were found to have positively flowering response to the lighting treatment. The duration of night-breaking treatment for successful flowering initiation varied from 33- 48 days. The lighting-sensitive genotypes bore 1-2 flowering flushes. Floral and fruiting stages took 21-26 and 46-59 days, respectively. Among sixteen fruiting genotypes, the highest fruit set rates were found in Damao 9, D4, D13, Chaozou large, Chaozhou 5, Small Nick and F22. Five cultivars and clones (Orejona, D4, Chaozhou large, Chaozhou 5 and Small Nick) produced fruits with an average weight of more than 300 g per fruit which were higher than those of the fruits formed in the summer of 2013. Fruits produced during off-season containing total soluble solids (TSS) from 17.5 to 20.7oBrix, which were higher than those produced inseason.

Keywords: Flowering response, long-day plant, night-breaking treatment, off-season production, pitaya.

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1066 Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method

Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).

Keywords: Homotopy perturbation method, Exact solution, Cauchy problem, inhomogeneous wave equation

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1065 Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation

Authors: Kew Lee Ming, Norhashidah Hj. Mohd. Ali

Abstract:

In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.

Keywords: Telegraph equation, explicit group iterative scheme, domain decomposition algorithm, parallelization.

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1064 Modeling and Numerical Simulation of Sound Radiation by the Boundary Element Method

Authors: Costa, E.S., Borges, E.N.M., Afonso, M.M.

Abstract:

The modeling of sound radiation is of fundamental importance for understanding the propagation of acoustic waves and, consequently, develop mechanisms for reducing acoustic noise. The propagation of acoustic waves, are involved in various phenomena such as radiation, absorption, transmission and reflection. The radiation is studied through the linear equation of the acoustic wave that is obtained through the equation for the Conservation of Momentum, equation of State and Continuity. From these equations, is the Helmholtz differential equation that describes the problem of acoustic radiation. In this paper we obtained the solution of the Helmholtz differential equation for an infinite cylinder in a pulsating through free and homogeneous. The analytical solution is implemented and the results are compared with the literature. A numerical formulation for this problem is obtained using the Boundary Element Method (BEM). This method has great power for solving certain acoustical problems in open field, compared to differential methods. BEM reduces the size of the problem, thereby simplifying the input data to be worked and reducing the computational time used.

Keywords: Acoustic radiation, boundary element

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1063 Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method

Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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1062 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming

Authors: N. Kumaresan, J. Kavikumar, M. Kumudthaa, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by genetic programming (GP). The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, Genetic programming and H-difference.

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1061 A Schur Method for Solving Projected Continuous-Time Sylvester Equations

Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

Abstract:

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

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1060 Crank-Nicolson Difference Scheme for the Generalized Rosenau-Burgers Equation

Authors: Kelong Zheng, Jinsong Hu,

Abstract:

In this paper, numerical solution for the generalized Rosenau-Burgers equation is considered and Crank-Nicolson finite difference scheme is proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence and priori error estimate of the scheme are proved. Numerical results demonstrate that the scheme is efficient and reliable.

Keywords: Generalized Rosenau-Burgers equation, difference scheme, stability, convergence.

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1059 Stability of Stochastic Model Predictive Control for Schrödinger Equation with Finite Approximation

Authors: Tomoaki Hashimoto

Abstract:

Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: Optimal control, stochastic systems, quantum systems, stabilization.

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1058 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories

Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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1057 Complex Fuzzy Evolution Equation with Nonlocal Conditions

Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

Abstract:

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups.

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1056 An Asymptotic Solution for the Free Boundary Parabolic Equations

Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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1055 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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1054 Periodic Solutions for a Higher Order Nonlinear Neutral Functional Differential Equation

Authors: Yanling Zhu

Abstract:

In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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1053 Optimal Relaxation Parameters for Obtaining Efficient Iterative Methods for the Solution of Electromagnetic Scattering Problems

Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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1052 An H1-Galerkin Mixed Method for the Coupled Burgers Equation

Authors: Xianbiao Jia, Hong Li, Yang Liu, Zhichao Fang

Abstract:

In this paper, an H1-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived.

Keywords: The coupled Burgers equation, H1-Galerkin mixed finite element method, Backward Euler's method, Optimal error estimates.

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1051 An Examination and Validation of the Theoretical Resistivity-Temperature Relationship for Conductors

Authors: Fred Lacy

Abstract:

Electrical resistivity is a fundamental parameter of metals or electrical conductors. Since resistivity is a function of temperature, in order to completely understand the behavior of metals, a temperature dependent theoretical model is needed. A model based on physics principles has recently been developed to obtain an equation that relates electrical resistivity to temperature. This equation is dependent upon a parameter associated with the electron travel time before being scattered, and a parameter that relates the energy of the atoms and their separation distance. Analysis of the energy parameter reveals that the equation is optimized if the proportionality term in the equation is not constant but varies over the temperature range. Additional analysis reveals that the theoretical equation can be used to determine the mean free path of conduction electrons, the number of defects in the atomic lattice, and the ‘equivalent’ charge associated with the metallic bonding of the atoms. All of this analysis provides validation for the theoretical model and provides insight into the behavior of metals where performance is affected by temperatures (e.g., integrated circuits and temperature sensors).

Keywords: Callendar–van Dusen, conductivity, mean free path, resistance temperature detector, temperature sensor.

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1050 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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1049 Effect of the Rise/Span Ratio of a Spherical Cap Shell on the Buckling Load

Authors: Peter N. Khakina, Mohammed I. Ali, Enchun Zhu, Huazhang Zhou, Baydaa H. Moula

Abstract:

Rise/span ratio has been mentioned as one of the reasons which contribute to the lower buckling load as compared to the Classical theory buckling load but this ratio has not been quantified in the equation. The purpose of this study was to determine a more realistic buckling load by quantifying the effect of the rise/span ratio because experiments have shown that the Classical theory overestimates the load. The buckling load equation was derived based on the theorem of work done and strain energy. Thereafter, finite element modeling and simulation using ABAQUS was done to determine the variables that determine the constant in the derived equation. The rise/span was found to be the determining factor of the constant in the buckling load equation. The derived buckling load correlates closely to the load obtained from experiments.

Keywords: Buckling, Finite element, Rise/span ratio, Sphericalcap

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1048 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation

Authors: Xiguang Li

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.

Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.

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1047 A Fast Cyclic Reduction Algorithm for A Quadratic Matrix Equation Arising from Overdamped Systems

Authors: Ning Dong, Bo Yu

Abstract:

We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algorithm.

Keywords: Fast algorithm, Cyclic reduction, Overdampedquadratic matrix equation, Structure-preserving doubling algorithm

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1046 New High Order Group Iterative Schemes in the Solution of Poisson Equation

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: Explicit group iterative method, finite difference, fourth order compact, Poisson equation.

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1045 A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions

Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.

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1044 The Effects of Tissue Optical Parameters and Interface Reflectivity on Light Diffusion in Biological Tissues

Authors: MA. Ansari

Abstract:

In cancer progress, the optical properties of tissues like absorption and scattering coefficient change, so by these changes, we can trace the progress of cancer, even it can be applied for pre-detection of cancer. In this paper, we investigate the effects of changes of optical properties on light penetrated into tissues. The diffusion equation is widely used to simulate light propagation into biological tissues. In this study, the boundary integral method (BIM) is used to solve the diffusion equation. We illustrate that the changes of optical properties can modified the reflectance or penetrating light.

Keywords: Diffusion equation, boundary element method, refractive index

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1043 Unique Positive Solution of Nonlinear Fractional Differential Equation Boundary Value Problem

Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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1042 Hyers-Ulam Stability of Functional Equationf(3x) = 4f(3x − 3) + f(3x − 6)

Authors: Soon-Mo Jung

Abstract:

The functional equation f(3x) = 4f(3x-3)+f(3x- 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X, where X is a real Banach space.

Keywords: Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

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1041 Ginzburg-Landau Model : an Amplitude Evolution Equation for Shallow Wake Flows

Authors: Imad Chaddad, Andrei A. Kolyshkin

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory.

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