**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**4954

# Search results for: nonlinear boundary problem

##### 4954 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.

##### 4953 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.

##### 4952 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.

##### 4951 Solving the Nonlinear Heat Conduction in a Spherical Coordinate with Electrical Simulation

**Authors:**
A. M. Gheitaghy,
H. Saffari,
G. Q. Zhang

**Abstract:**

_{rc}, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method is found to be good.

**Keywords:**
Convective boundary,
radiative boundary,
electrical simulation method,
nonlinear heat conduction,
spherical coordinate.

##### 4950 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.

##### 4949 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

##### 4948 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.

##### 4947 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.

##### 4946 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.

##### 4945 Quasilinearization–Barycentric Approach for Numerical Investigation of the Boundary Value Fin Problem

**Authors:**
Alireza Rezaei,
Fatemeh Baharifard,
Kourosh Parand

**Abstract:**

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

**Keywords:**
Quasilinearization method,
Barycentric lagrange interpolation,
nonlinear ODE,
fin problem,
heat transfer.

##### 4944 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.

##### 4943 Radiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction

**Authors:**
Motahar Reza,
Rajni Chahal,
Neha Sharma

**Abstract:**

This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

**Keywords:**
Boundary layer flow,
nonlinear stretching,
Casson fluid,
heat transfer,
radiation.

##### 4942 The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term

**Authors:**
Jaipong Kasemsuwan

**Abstract:**

**Keywords:**
Finite-difference method,
the nonlinear damped
equation,
the numerical simulation,
the suspended string equation

##### 4941 Dynamic Analysis of Nonlinear Models with Infinite Extension by Boundary Elements

**Authors:**
Delfim Soares Jr.,
Webe J. Mansur

**Abstract:**

**Keywords:**
Boundary Element Method,
Dynamic Elastoplastic
Analysis,
Iterative Coupling,
Multiple Time-Steps.

##### 4940 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.

##### 4939 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.

##### 4938 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.

##### 4937 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.

##### 4936 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition

**Abstract:**

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

**Keywords:**
Fractional differential equation,
Integral boundary condition,
Schauder fixed point theorem,
Banach contraction principle.

##### 4935 Numerical Solutions of Boundary Layer Flow over an Exponentially Stretching/Shrinking Sheet with Generalized Slip Velocity

**Authors:**
Ezad Hafidz Hafidzuddin,
Roslinda Nazar,
Norihan M. Arifin,
Ioan Pop

**Abstract:**

In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

**Keywords:**
Boundary Layer,
Exponentially Stretching/Shrinking
Sheet,
Generalized Slip,
Heat Transfer,
Numerical Solutions.

##### 4934 Spectral Investigation for Boundary Layer Flow over a Permeable Wall in the Presence of Transverse Magnetic Field

**Authors:**
Saeed Sarabadan,
Mehran Nikarya,
Kouroah Parand

**Abstract:**

**Keywords:**
MHD Falkner-Skan,
nonlinear ODE,
spectral
collocation method,
Bessel functions,
skin friction,
velocity.

##### 4933 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

##### 4932 Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

**Authors:**
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
positive solution,
existence and uniqueness,
fixed point theorem,
generalized concave
and convex operator,
integral boundary conditions.

##### 4931 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.

##### 4930 Partial Stabilization of a Class of Nonlinear Systems Via Center Manifold Theory

**Authors:**
Ping He

**Abstract:**

**Keywords:**
Partial stabilization,
Nonlinear critical systems,
Centermanifold theory,
Lyapunov function,
System reduction.

##### 4929 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.

##### 4928 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.

##### 4927 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.

##### 4926 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.

##### 4925 Nonlinear Model Predictive Swing-Up and Stabilizing Sliding Mode Controllers

**Authors:**
S. Kahvecioglu,
A. Karamancioglu,
A. Yazici

**Abstract:**

**Keywords:**
Inverted pendulum,
model predictive control,
swingup,
stabilization.