International Journal of Engineering, Mathematical and Physical Sciences

Complexity Reduction Approach with Jacobi Iterative Method for Solving Composite Trapezoidal Algebraic Equations

Year: 2013 Volume: 7 Issue: 3 525 - 529 Pages

Abstract: In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Septic B-Spline Collocation Method for Numerical Solution of the Kuramoto-Sivashinsky Equation

Year: 2013 Volume: 7 Issue: 3 520 - 524 Pages

Abstract: In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Cubic B-spline Collocation Method for Numerical Solution of the Benjamin-Bona-Mahony-Burgers Equation

Year: 2013 Volume: 7 Issue: 3 516 - 519 Pages

Abstract: In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

Absolute Cross Sections of Multi-Photon Ionization of Xenon by the Comparison with Process of its Electron-Impact Ionization

Year: 2013 Volume: 7 Issue: 11 1566 - 1568 Pages

Abstract: Comparison of electron- and photon-impact processes as a method for determination of photo-ionization cross sections is described, discussed and shown to have many attractive features.

Proximal Parallel Alternating Direction Method for Monotone Structured Variational Inequalities

Year: 2013 Volume: 7 Issue: 3 511 - 515 Pages

Authors:
Min Sun
Jing Liu

Abstract: In this paper, we focus on the alternating direction method, which is one of the most effective methods for solving structured variational inequalities(VI). In fact, we propose a proximal parallel alternating direction method which only needs to solve two strongly monotone sub-VI problems at each iteration. Convergence of the new method is proved under mild assumptions. We also present some preliminary numerical results, which indicate that the new method is quite efficient.

Enhanced Gram-Schmidt Process for Improving the Stability in Signal and Image Processing

Year: 2013 Volume: 7 Issue: 3 506 - 510 Pages

Abstract: The Gram-Schmidt Process (GSP) is used to convert a non-orthogonal basis (a set of linearly independent vectors) into an orthonormal basis (a set of orthogonal, unit-length vectors). The process consists of taking each vector and then subtracting the elements in common with the previous vectors. This paper introduces an Enhanced version of the Gram-Schmidt Process (EGSP) with inverse, which is useful for signal and image processing applications.

Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

Year: 2013 Volume: 7 Issue: 3 501 - 505 Pages

Authors:
Mahdi Nouri

Abstract: In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Existence of Periodic Solution for p-Laplacian Neutral Rayleigh Equation with Sign-variable Coefficient of Non Linear Term

Year: 2013 Volume: 7 Issue: 3 493 - 500 Pages

Abstract: As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change signs in this paper, which are different from the corresponding ones of known literature.

Almost Periodic Solution for an Impulsive Neural Networks with Distributed Delays

Year: 2013 Volume: 7 Issue: 3 483 - 492 Pages

Authors:
Lili Wang

Abstract: By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and effectiveness of the results.

Jacobi-Based Methods in Solving Fuzzy Linear Systems

Year: 2013 Volume: 7 Issue: 3 476 - 482 Pages

Abstract: Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

Periodic Solutions for a Food Chain System with Monod–Haldane Functional Response on Time Scales

Year: 2013 Volume: 7 Issue: 3 472 - 475 Pages

Abstract: In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay

Year: 2013 Volume: 7 Issue: 3 462 - 471 Pages

Abstract: In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.

Spline Basis Neural Network Algorithm for Numerical Integration

Year: 2013 Volume: 7 Issue: 3 458 - 461 Pages

Abstract: A new basis function neural network algorithm is proposed for numerical integration. The main idea is to construct neural network model based on spline basis functions, which is used to approximate the integrand by training neural network weights. The convergence theorem of the neural network algorithm, the theorem for numerical integration and one corollary are presented and proved. The numerical examples, compared with other methods, show that the algorithm is effective and has the characteristics such as high precision and the integrand not required known. Thus, the algorithm presented in this paper can be widely applied in many engineering fields.

Multiple Positive Periodic Solutions of a Delayed Predatory-Prey System with Holling Type II Functional Response

Year: 2013 Volume: 7 Issue: 3 453 - 457 Pages

Abstract: In this letter, we considers a delayed predatory-prey system with Holling type II functional response. Under some sufficient conditions, the existence of multiple positive periodic solutions is obtained by using Mawhin’s continuation theorem of coincidence degree theory. An example is given to illustrate the effectiveness of our results.

Permanence and Global Attractivity of a Delayed Predator-Prey Model with Mutual Interference

Year: 2013 Volume: 7 Issue: 3 446 - 452 Pages

Authors:
Kai Wang
Yanling Zu

Abstract: By utilizing the comparison theorem and Lyapunov second method, some sufficient conditions for the permanence and global attractivity of positive periodic solution for a predator-prey model with mutual interference m ∈ (0, 1) and delays τi are obtained. It is the first time that such a model is considered with delays. The significant is that the results presented are related to the delays and the mutual interference constant m. Several examples are illustrated to verify the feasibility of the results by simulation in the last part.

Semiconvergence of Alternating Iterative Methods for Singular Linear Systems

Year: 2013 Volume: 7 Issue: 3 441 - 445 Pages

Authors:
Jing Wu

Abstract: In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.

Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Year: 2013 Volume: 7 Issue: 3 436 - 440 Pages

Authors:
Jing Li
Guang Zhou

Abstract: Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

Year: 2013 Volume: 7 Issue: 2 312 - 314 Pages

Abstract: Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

A Special Algorithm to Approximate the Square Root of Positive Integer

Year: 2013 Volume: 7 Issue: 2 308 - 311 Pages

Authors:
Hsian Ming Goo

Abstract: The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Explicit Solutions and Stability of Linear Differential Equations with multiple Delays

Year: 2013 Volume: 7 Issue: 2 300 - 307 Pages

Authors:
Felix Che Shu

Abstract: We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.