**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**6571

# Search results for: Boundary value problem; Multipoint equation boundary value problems

##### 6571 An Efficient Method for Solving Multipoint Equation Boundary Value Problems

**Authors:**
Ampon Dhamacharoen,
Kanittha Chompuvised

**Abstract:**

**Keywords:**
Boundary value problem; Multipoint equation
boundary value problems,
Shooting Method,
Newton-Broyden
method.

##### 6570 Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition

**Authors:**
Theddeus T. Akano,
Omotayo A. Fakinlede

**Abstract:**

**Keywords:**
Sturm-Liouville problem,
Robin boundary condition,
finite element method,
eigenvalue problems.

##### 6569 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.

##### 6568 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)

**Authors:**
Li Ge

**Abstract:**

**Keywords:**
impulsive differential equations,
impulsive integraldifferential equation,
boundary value problems

##### 6567 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.

##### 6566 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm

**Authors:**
U. C. Amadi,
N. A. Udoh

**Abstract:**

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

**Keywords:**
Ying Buzu Shu,
nonlinear boundary problem,
Taylor series algorithm,
infinite series.

##### 6565 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.

##### 6564 Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions

**Authors:**
Alexandra Leukauf,
Alexander Schirrer,
Emir Talic

**Abstract:**

**Keywords:**
Absorbing boundary conditions,
boundary control,
Fourier Galerkin approach,
modal approach,
wave equation.

##### 6563 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
Fengxia Zheng,
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
Boundary value
problem,
Positive solution,
Existence and uniqueness,
Fixed point
theorem of a sum operator.

##### 6562 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

##### 6561 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Chuanyun Gu,
Shouming Zhong

**Abstract:**

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

**Keywords:**
Fractional differential equation,
Boundary value problem,
Positive solution,
Existence and uniqueness,
Fixed point theorem of a sum operator

##### 6560 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation

**Authors:**
Aziz Sezgin

**Abstract:**

**Keywords:**
Backstepping,
boundary control,
2-D,
3-D,
n-D heat
equation,
distributed parameter systems.

##### 6559 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

**Authors:**
Thanin Sitthiwirattham,
Jiraporn Reunsumrit

**Abstract:**

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

**Keywords:**
Positive solution,
Boundary value problem,
Fixed
point theorem,
Cone.

##### 6558 Genetic Algorithm Approach for Solving the Falkner–Skan Equation

**Authors:**
Indu Saini,
Phool Singh,
Vikas Malik

**Abstract:**

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Genetic Algorithm is used to calculate shooting angle. The initial value problems arisen during shooting are computed by Runge-Kutta Fehlberg method. The numerical solutions obtained by the present method are in agreement with those obtained by previous authors.

**Keywords:**
Boundary Layer Flow,
Falkner–Skan equation,
Genetic Algorithm,
Shooting method.

##### 6557 Variational Iteration Method for the Solution of Boundary Value Problems

**Authors:**
Olayiwola M.O.,
Gbolagade A .W.,
Akinpelu F. O.

**Abstract:**

In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.

**Keywords:**
Variational iteration method,
boundary value
problems,
convergence,
restricted variation.

##### 6556 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

**Authors:**
V. Ghadamyari,
F. Samadi,
F. Kowsary

**Abstract:**

**Keywords:**
Boundary elements,
Conjugate Gradient Method,
Inverse Geometry Problem,
Sensitivity equation.

##### 6555 Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem

**Authors:**
S. N. Hosseini,
S. M. H. Karimian

**Abstract:**

A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.

**Keywords:**
Immersed Boundary Method,
conservation of mass and momentum laws,
moving boundary,
boundary condition.

##### 6554 On Method of Fundamental Solution for Nondestructive Testing

**Abstract:**

**Keywords:**
ill-posed,
TSVD,
Laplace's equation,
inverse problem,
L-curve,
Generalized Cross Validation.

##### 6553 Comparison Results of Two-point Fuzzy Boundary Value Problems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

**Keywords:**
Fuzzy derivative,
lateral type of H-derivative,
fuzzy differential equations,
fuzzy boundary value problems,
boundary value problems.

##### 6552 Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method

**Authors:**
M. A. Ghorbani,
M. Pasbani Khiavi

**Abstract:**

**Keywords:**
Reservoir,
finite element,
truncated boundary,
hydrodynamic pressure

##### 6551 Existence of Solution for Boundary Value Problems of Differential Equations with Delay

**Authors:**
Xiguang Li

**Abstract:**

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

**Keywords:**
Banach space,
boundary value problem,
differential equation,
delay.

##### 6550 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.

##### 6549 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)

**Authors:**
Li Ge

**Abstract:**

**Keywords:**
impulsive differential equations,
impulsive integraldifferentialequation,
boundary value problems

##### 6548 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)

**Authors:**
Li Ge

**Abstract:**

**Keywords:**
impulsive differential equations,
impulsive integraldifferentialequation,
boundary value problems

##### 6547 An Asymptotic Formula for Pricing an American Exchange Option

**Authors:**
Hsuan-Ku Liu

**Abstract:**

In this paper, the American exchange option (AEO) valuation problem is modelled as a free boundary problem. The critical stock price for an AEO is satisfied an integral equation implicitly. When the remaining time is large enough, an asymptotic formula is provided for pricing an AEO. The numerical results reveal that our asymptotic pricing formula is robust and accurate for the long-term AEO.

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

##### 6546 Numerical Solution of a Laminar Viscous Flow Boundary Layer Equation Using Uniform Haar Wavelet Quasi-linearization Method

**Authors:**
Harpreet Kaur,
Vinod Mishra,
R. C. Mittal

**Abstract:**

In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of hydrodynamics and in fluid mechanics of laminar viscous flows. Quasi-linearization is iterative process but our proposed technique gives excellent numerical results with quasilinearization for solving nonlinear differential equations without any iteration on selecting collocation points by Haar wavelets. We have solved Blasius equation for 1≤α ≤ 2 and the numerical results are compared with the available results in literature. Finally, we conclude that proposed method is a promising tool for solving the well known nonlinear Blasius equation.

**Keywords:**
Boundary layer Blasius equation,
collocation points,
quasi-linearization process,
uniform haar wavelets.

##### 6545 Non-reflection Boundary Conditions for Numerical Simulation of Supersonic Flow

**Authors:**
A. Abdalla,
A. Kaltayev

**Abstract:**

This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.

**Keywords:**
WENO scheme,
non-reflection boundary conditions,
NSCBC,
supersonic flow.

##### 6544 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

**Authors:**
Talaat S. El-Danaf

**Abstract:**

**Keywords:**
Quartic nonpolynomial spline,
Two-point boundary
value problem.

##### 6543 Approximated Solutions of Two-Point Nonlinear Boundary Problem by a Combination of Taylor Series Expansion and Newton Raphson Method

**Authors:**
Chinwendu. B. Eleje,
Udechukwu P. Egbuhuzor

**Abstract:**

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

**Keywords:**
Newton Raphson method,
non-linear boundary value problem,
Taylor series approximation,
Michaelis-Menten equation.

##### 6542 The Performance of Alternating Top-Bottom Strategy for Successive Over Relaxation Scheme on Two Dimensional Boundary Value Problem

**Authors:**
M. K. Hasan,
Y. H. Ng,
J. Sulaiman

**Abstract:**

This paper present the implementation of a new ordering strategy on Successive Overrelaxation scheme on two dimensional boundary value problems. The strategy involve two directions alternatingly; from top and bottom of the solution domain. The method shows to significantly reduce the iteration number to converge. Four numerical experiments were carried out to examine the performance of the new strategy.

**Keywords:**
Two dimensional boundary value problems,
Successive Overrelaxation scheme,
Alternating Top-Bottom strategy,
fast convergence