**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1563

# Search results for: Hammerstein integral equations

##### 1563 Numerical Solution of Hammerstein Integral Equations by Using Quasi-Interpolation

**Authors:**
M. Zarebnia,
S. Khani

**Abstract:**

In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

**Keywords:**
Hammerstein integral equations,
quasi-interpolation,
Nystrom’s method.

##### 1562 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

**Authors:**
N. Parandin,
M. A. Fariborzi Araghi

**Abstract:**

**Keywords:**
Fuzzy function integral equations,
Iterative method,
Linear systems,
Parametric form of fuzzy number.

##### 1561 Optimization Approach to Estimate Hammerstein–Wiener Nonlinear Blocks in Presence of Noise and Disturbance

**Authors:**
Leili Esmaeilani,
Jafar Ghaisari,
Mohsen Ahmadian

**Abstract:**

**Keywords:**
Identification,
Hammerstein-Wiener,
optimization,
quantization.

##### 1560 Integral Image-Based Differential Filters

**Authors:**
Kohei Inoue,
Kenji Hara,
Kiichi Urahama

**Abstract:**

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

**Keywords:**
Integral images,
differential images,
differential filters,
image fusion.

##### 1559 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
Convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations.

##### 1558 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

**Authors:**
jianhua Hou,
Changqing Yang,
and Beibo Qin

**Abstract:**

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

**Keywords:**
Hybrid functions,
Fredholm integral equation,
Blockpulse,
Chebyshev polynomials,
product operational matrix.

##### 1557 High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method

**Authors:**
Pan Cheng,
Jin Huang,
Guang Zeng

**Abstract:**

**Keywords:**
boundary integral equation,
extrapolation algorithm,
aposteriori error estimate,
elasticity.

##### 1556 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

**Authors:**
M. Abdulkawi,
Z. K. Eshkuvatov,
N. M. A. Nik Long

**Abstract:**

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

**Keywords:**
Singular integral equations,
Cauchy kernel,
Chebyshev polynomials,
interpolation.

##### 1555 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

**Authors:**
Akbar H. Borzabadi,
Omid S. Fard

**Abstract:**

**Keywords:**
Fredholm integral equation,
Optimization method,
Optimal control,
Nonlinear and linear programming

##### 1554 Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model

**Authors:**
A. Brouri,
F. Giri,
A. Mkhida,
F. Z. Chaoui,
A. Elkarkri,
M. L. Chhibat

**Abstract:**

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

**Keywords:**
Nonlinear system identification,
Hammerstein systems,
Wiener systems,
frequency identification.

##### 1553 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 1552 Research of a Multistep Method Applied to Numerical Solution of Volterra Integro-Differential Equation

**Authors:**
M.Imanova,
G.Mehdiyeva,
V.Ibrahimov

**Abstract:**

**Keywords:**
Volterra integro-differential equations,
multistepmethods,
finite-difference methods,
initial value problem

##### 1551 Modeling and Identification of Hammerstein System by using Triangular Basis Functions

**Authors:**
K. Elleuch,
A. Chaari

**Abstract:**

**Keywords:**
Identification,
Hammerstein model,
Piecewisenonlinear characteristic,
Dead-zone nonlinearity,
Triangular basisfunctions,
Singular Values Decomposition

##### 1550 Solution of First kind Fredholm Integral Equation by Sinc Function

**Authors:**
Khosrow Maleknejad,
Reza Mollapourasl,
Parvin Torabi,
Mahdiyeh Alizadeh,

**Abstract:**

**Keywords:**
Integral equation,
Fredholm type,
Collocation method,
Sinc approximation.

##### 1549 Complexity Reduction Approach with Jacobi Iterative Method for Solving Composite Trapezoidal Algebraic Equations

**Authors:**
Mohana Sundaram Muthuvalu,
Jumat Sulaiman

**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.

**Keywords:**
Complexity reduction approach,
Composite trapezoidal
scheme,
Jacobi method,
Linear Fredholm integral equations

##### 1548 The Particle Swarm Optimization Against the Runge’s Phenomenon: Application to the Generalized Integral Quadrature Method

**Authors:**
A. Zerarka,
A. Soukeur,
N. Khelil

**Abstract:**

In the present work, we introduce the particle swarm optimization called (PSO in short) to avoid the Runge-s phenomenon occurring in many numerical problems. This new approach is tested with some numerical examples including the generalized integral quadrature method in order to solve the Volterra-s integral equations

**Keywords:**
Integral equation,
particle swarm optimization,
Runge's phenomenon.

##### 1547 On One Application of Hybrid Methods For Solving Volterra Integral Equations

**Authors:**
G.Mehdiyeva,
V.Ibrahimov,
M.Imanova

**Abstract:**

**Keywords:**
Volterra integral equation,
hybrid methods,
stability
and degree,
methods of quadrature

##### 1546 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.

##### 1545 On-line Identification of Continuous-time Hammerstein Systems via RBF Networks and Immune Algorithm

**Authors:**
Tomohiro Hachino,
Kengo Nagatomo,
Hitoshi Takata

**Abstract:**

**Keywords:**
Continuous-time System,
Hammerstein System,
OnlineIdentification,
Immune Algorithm,
RBF network.

##### 1544 Hybrid Algorithm for Hammerstein System Identification Using Genetic Algorithm and Particle Swarm Optimization

**Authors:**
Tomohiro Hachino,
Kenji Shimoda,
Hitoshi Takata

**Abstract:**

**Keywords:**
Hammerstein system,
identification,
automatic choosing
function model,
genetic algorithm,
particle swarm optimization.

##### 1543 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations

**Authors:**
Fuziyah Ishak,
Siti Norazura Ahmad

**Abstract:**

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

**Keywords:**
Accuracy,
extended trapezoidal method,
numerical solution,
Volterra integro-differential equations.

##### 1542 Mechanical Quadrature Methods and Their Extrapolations for Solving First Kind Boundary Integral Equations of Anisotropic Darcy-s Equation

**Authors:**
Xin Luo,
Jin Huang,
Chuan-Long Wang

**Abstract:**

The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

**Keywords:**
Darcy's equation,
anisotropic,
mechanical quadrature methods,
extrapolation methods,
a posteriori error estimate.

##### 1541 Mechanical Quadrature Methods for Solving First Kind Boundary Integral Equations of Stationary Stokes Problem

**Authors:**
Xin Luo,
Jin Huang,
Pan Cheng

**Abstract:**

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

**Keywords:**
Stokes problem,
boundary integral equation,
mechanical
quadrature methods,
asymptotic expansions.

##### 1540 Displacement Solution for a Static Vertical Rigid Movement of an Interior Circular Disc in a Transversely Isotropic Tri-Material Full-Space

**Authors:**
D. Mehdizadeh,
M. Rahimian,
M. Eskandari-Ghadi

**Abstract:**

This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.

**Keywords:**
Transversely isotropic,
rigid disc,
elasticity,
dual integral equations,
tri-material full-space.

##### 1539 Numerical Solution of Infinite Boundary Integral Equation by Using Galerkin Method with Laguerre Polynomials

**Authors:**
N. M. A. Nik Long,
Z. K. Eshkuvatov,
M. Yaghobifar,
M. Hasan

**Abstract:**

In this paper the exact solution of infinite boundary integral equation (IBIE) of the second kind with degenerate kernel is presented. Moreover Galerkin method with Laguerre polynomial is applied to get the approximate solution of IBIE. Numerical examples are given to show the validity of the method presented.

**Keywords:**
Approximation,
Galerkin method,
Integral
equations,
Laguerre polynomial.

##### 1538 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra

**Authors:**
Ali Shojaei-Fard

**Abstract:**

**Keywords:**
Birkhoff Factorization,
Connes-Kreimer Hopf Algebra of Rooted Trees,
Integral Renormalization,
Lax Pair Equation,
Rota- Baxter Algebras.

##### 1537 On Fourier Type Integral Transform for a Class of Generalized Quotients

**Authors:**
A. S. Issa,
S. K. Q. AL-Omari

**Abstract:**

**Keywords:**
Fourier type integral,
Fourier integral,
generalized
quotient,
Boehmian,
distribution.

##### 1536 The Application of Hybrid Orthonomal Bernstein and Block-Pulse Functions in Finding Numerical Solution of Fredholm Fuzzy Integral Equations

**Authors:**
Mahmoud Zarrini,
Sanaz Torkaman

**Abstract:**

In this paper, we have proposed a numerical method for solving fuzzy Fredholm integral equation of the second kind. In this method a combination of orthonormal Bernstein and Block-Pulse functions are used. In most cases, the proposed method leads to the exact solution. The advantages of this method are shown by an example and calculate the error analysis.

**Keywords:**
Fuzzy Fredholm Integral Equation,
Bernstein,
Block-Pulse,
Orthonormal.

##### 1535 Integral Methods in the Determination of Temperature Fields of Cooled Blades of Gas Turbines

**Authors:**
C. Ardil

**Abstract:**

**Keywords:**
Integral methods,
determination of temperature fields,
cooled blades,
gas turbines.

##### 1534 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

**Authors:**
Adil AL-Rammahi

**Abstract:**

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

**Keywords:**
Fredholm integral equation,
power series,
Banach fixed point theorem,
Linear Systems.