**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4134

# Search results for: two-point boundary value problem

##### 4134 Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials

**Authors:**
Sanjeeb Kumar Kar

**Abstract:**

**Keywords:**
Optimal control,
linear systems,
distributed parametersystems,
Legendre polynomials.

##### 4133 Sliding Mode Control with Fuzzy Boundary Layer to Air-Air Interception Problem

**Authors:**
Mustafa Resa Becan

**Abstract:**

The performance of a type of fuzzy sliding mode control is researched by considering the nonlinear characteristic of a missile-target interception problem to obtain a robust interception process. The variable boundary layer by using fuzzy logic is proposed to reduce the chattering around the switching surface then is applied to the interception model which was derived. The performances of the sliding mode control with constant and fuzzy boundary layer are compared at the end of the study and the results are evaluated.

**Keywords:**
Sliding mode control,
fuzzy,
boundary layer,
interception problem.

##### 4132 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.

##### 4131 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.

##### 4130 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.

##### 4129 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.

##### 4128 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.

##### 4127 An Alternative Proof for the NP-completeness of Top Right Access point-Minimum Length Corridor Problem

**Authors:**
Priyadarsini P.L.K,
Hemalatha T.

**Abstract:**

In the Top Right Access point Minimum Length Corridor (TRA-MLC) problem [1], a rectangular boundary partitioned into rectilinear polygons is given and the problem is to find a corridor of least total length and it must include the top right corner of the outer rectangular boundary. A corridor is a tree containing a set of line segments lying along the outer rectangular boundary and/or on the boundary of the rectilinear polygons. The corridor must contain at least one point from the boundaries of the outer rectangle and also the rectilinear polygons. Gutierrez and Gonzalez [1] proved that the MLC problem, along with some of its restricted versions and variants, are NP-complete. In this paper, we give a shorter proof of NP-Completeness of TRA-MLC by findig the reduction in the following way.

**Keywords:**
NP-complete,
2-connected planar graph,
Grid embedding of a plane graph.

##### 4126 Positive Solutions for Discrete Third-order Three-point Boundary Value Problem

**Authors:**
Benshi Zhu

**Abstract:**

**Keywords:**
Positive solutions,
Discrete boundary value problem,
Third-order,
Three-point,
Algebraic topology

##### 4125 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.

##### 4124 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.

##### 4123 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.

##### 4122 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.

##### 4121 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.

##### 4120 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.

##### 4119 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

##### 4118 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

**Authors:**
Nur Nadiah Abd Hamid,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail

**Abstract:**

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

**Keywords:**
two-point boundary value problem,
B-spline,
extendedcubic B-spline.

##### 4117 Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic Boundary Value Problem −Δu = f(u)

**Authors:**
Abida Harbi

**Abstract:**

**Keywords:**
Error estimates,
Finite elements,
Nonlinear PDEs,
Schwarz method.

##### 4116 The Design of Axisymmetric Ducts for Incompressible Flow with a Parabolic Axial Velocity Inlet Profile

**Authors:**
V.Pavlika

**Abstract:**

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

**Keywords:**
Inverse problem,
irrotational incompressible flow,
Boundary value problem.

##### 4115 A Reproduction of Boundary Conditions in Three-Dimensional Continuous Casting Problem

**Authors:**
Iwona Nowak,
Jacek Smolka,
Andrzej J. Nowak

**Abstract:**

The paper discusses a 3D numerical solution of the inverse boundary problem for a continuous casting process of alloy. The main goal of the analysis presented within the paper was to estimate heat fluxes along the external surface of the ingot. The verified information on these fluxes was crucial for a good design of a mould, effective cooling system and generally the whole caster. In the study an enthalpy-porosity technique implemented in Fluent package was used for modeling the solidification process. In this method, the phase change interface was determined on the basis of the liquid fraction approach. In inverse procedure the sensitivity analysis was applied for retrieving boundary conditions. A comparison of the measured and retrieved values showed a high accuracy of the computations. Additionally, the influence of the accuracy of measurements on the estimated heat fluxes was also investigated.

**Keywords:**
Boundary inverse problem,
sensitivity analysis,
continuous casting,
numerical simulation.

##### 4114 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.

##### 4113 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.

##### 4112 Recovering the Boundary Data in the Two Dimensional Inverse Heat Conduction Problem Using the Ritz-Galerkin Method

**Authors:**
Saeed Sarabadan,
Kamal Rashedi

**Abstract:**

**Keywords:**
Inverse problem,
parabolic equations,
heat equation,
Ritz-Galerkin method,
Landweber iterations.

##### 4111 Fuzzy Boundary Layer Solution to Nonlinear Hydraulic Position Control Problem

**Authors:**
Mustafa Resa Becan

**Abstract:**

Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.

**Keywords:**
Hydraulic servomechanism,
position control,
sliding mode control,
chattering,
fuzzy boundary layer.

##### 4110 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.

##### 4109 The Algorithm to Solve the Extend General Malfatti’s Problem in a Convex Circular Triangle

**Authors:**
Ching-Shoei Chiang

**Abstract:**

The Malfatti’s problem solves the problem of fitting three circles into a right triangle such that these three circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s problem). Furthermore, the problem has been extended to have 1 + 2 + … + n circles inside the triangle with special tangency properties among circles and triangle sides; it is called the extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for the Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving the Tri(Tn) problem, n > 2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary as in Tri(Tn) problems. We call these problems the Carc(Tn) problems. The algorithm is a mO(Tn) algorithm, where m is the number of iterations in the loop. It takes less than 1000 iterations and less than 1 second for the Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties. This algorithm gives a solution for circle packing problem inside convex circular triangle with arbitrarily-sized circles. Many applications concerning circle packing may come from the result of the algorithm, such as logo design, architecture design, etc.

**Keywords:**
Circle packing,
computer-aided geometric design,
geometric constraint solver,
Malfatti’s problem.

##### 4108 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.

##### 4107 Topological Sensitivity Analysis for Reconstruction of the Inverse Source Problem from Boundary Measurement

**Authors:**
Maatoug Hassine,
Mourad Hrizi

**Abstract:**

**Keywords:**
Geometric inverse source problem,
heat equation,
topological sensitivity,
topological optimization,
Kohn-Vogelius
formulation.

##### 4106 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

##### 4105 Modeling and Simulating Human Arm Movement Using a 2 Dimensional 3 Segments Coupled Pendulum System

**Authors:**
Loay A. Al-Zu'be,
Asma A. Al-Tamimi,
Thakir D. Al-Momani,
Ayat J. Alkarala,
Maryam A. Alzawahreh

**Abstract:**

A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.

**Keywords:**
Body Configurations,
Equations of Motion,
Mathematical Modeling,
Movement Trajectories.