**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**47

# Search results for: boundary value problem

##### 47 Analytical Solution of the Boundary Value Problem of Delaminated Doubly-Curved Composite Shells

**Authors:**
András Szekrényes

**Abstract:**

Delamination is one of the major failure modes in laminated composite structures. Delamination tips are mostly captured by spatial numerical models in order to predict crack growth. This paper presents some mechanical models of delaminated composite shells based on shallow shell theories. The mechanical fields are based on a third-order displacement field in terms of the through-thickness coordinate of the laminated shell. The undelaminated and delaminated parts are captured by separate models and the continuity and boundary conditions are also formulated in a general way providing a large size boundary value problem. The system of differential equations is solved by the state space method for an elliptic delaminated shell having simply supported edges. The comparison of the proposed and a numerical model indicates that the primary indicator of the model is the deflection, the secondary is the widthwise distribution of the energy release rate. The model is promising and suitable to determine accurately the J-integral distribution along the delamination front. Based on the proposed model it is also possible to develop finite elements which are able to replace the computationally expensive spatial models of delaminated structures.

**Keywords:**
J-integral,
levy method,
third-order shell theory,
state space solution

##### 46 Rayleigh-Bénard-Taylor Convection of Newtonian Nanoliquid

**Authors:**
P. G. Siddheshwar,
T. N. Sakshath

**Abstract:**

**Keywords:**
Rotation,
nanoliquid,
rigid-rigid,
single-phase

##### 45 Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint

**Authors:**
M. Najafi,
F. Rahimi Dehgolan

**Abstract:**

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

**Keywords:**
Stability,
bifurcation,
non-linear vibration,
axially moving beam,
multiple scales method

##### 44 Analysis and Simulation of TM Fields in Waveguides with Arbitrary Cross-Section Shapes by Means of Evolutionary Equations of Time-Domain Electromagnetic Theory

**Authors:**
Ömer Aktaş,
Olga A. Suvorova,
Oleg Tretyakov

**Abstract:**

_{2}. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

**Keywords:**
analytical regularization method,
TM Field,
Arbitrary cross section waveguide,
evolutionary equations of electromagnetic theory of time-domain

##### 43 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:**
positive solution,
Fractional diﬀerential equation,
existence and uniqueness,
Boundary value
problem,
Fixed point
theorem of a sum operator

##### 42 Application of Higher Order Splines for Boundary Value Problems

**Authors:**
Pankaj Kumar Srivastava

**Abstract:**

**Keywords:**
Astrophysics,
thermal instability,
Septic spline,
Octic spline,
Nonic spline,
Tenth,
Eleventh,
Twelfth and Thirteenth Degree spline,
parametric and non-parametric
splines

##### 41 Dual Solutions in Mixed Convection Boundary Layer Flow: A Stability Analysis

**Authors:**
Anuar Ishak

**Abstract:**

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

**Keywords:**
Heat Transfer,
Stability Analysis,
mixed convection,
dual solutions

##### 40 Approximate Solution of Some Mixed Boundary Value Problems of the Generalized Theory of Couple-Stress Thermo-Elasticity

**Authors:**
M. Chumburidze,
D. Lekveishvili

**Abstract:**

We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

**Keywords:**
Boundary Value Problems,
The couple-stress thermo-elasticity

##### 39 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

**Authors:**
Anuar Ishak

**Abstract:**

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

**Keywords:**
Heat Transfer,
Stability Analysis,
dual solutions,
shrinking sheet

##### 38 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:**
boundary value problem,
positive solution,
cone,
Fixed
point theorem

##### 37 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

##### 36 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:**
boundary value problem,
positive solution,
fixed point theorem,
mixed monotone operator,
Fractional diﬀerential equation,
existence and uniqueness

##### 35 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:**
boundary value problem,
positive solution,
Fractional diﬀerential equation,
existence and uniqueness,
Fixed point theorem of a sum operator

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

**Authors:**
Abida Harbi

**Abstract:**

**Keywords:**
Finite elements,
nonlinear PDEs,
error estimates,
Schwarz method

##### 33 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
cone,
Banach space,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions

##### 32 An Application of the Sinc-Collocation Method to a Three-Dimensional Oceanography Model

**Authors:**
Y. Mohseniahouei,
K. Abdella,
M. Pollanen

**Abstract:**

**Keywords:**
Differential Equations,
Boundary Value Problems,
Wind-Driven Currents,
Sinc Numerical Methods

##### 31 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

**Keywords:**
cone,
Banach space,
fixed point index,
singular differential
equation

##### 30 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

**Keywords:**
cone,
Banach space,
fixed point index,
singular differential
equation

##### 29 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

##### 28 Stability of Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

**Keywords:**
Fractional Calculus,
Fractional diﬀerential equation,
Volterra integral equation,
Lane-Emden equation,
Riemann-Liouville fractional operators

##### 27 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:**
Genetic Algorithm,
boundary layer flow,
Shooting Method,
Falkner–Skan equation

##### 26 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:**
Convergence,
variational iteration method,
boundary value
problems,
restricted variation

##### 25 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
cone,
Banach space,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions

##### 24 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:**
Mathematical Modeling,
Equations of motion,
Body Configurations,
Movement Trajectories

##### 23 Note on the Necessity of the Patch Test

**Authors:**
Rado Flajs,
Miran Saje

**Abstract:**

We present a simple nonconforming approximation of the linear two–point boundary value problem which violates patch test requirements. Nevertheless the solutions, obtained from these type of approximations, converge to the exact solution.

**Keywords:**
Convergence,
generalized patch test,
Irons' patch test,
nonconforming finite element

##### 22 Linear Elasticity Problems Solved by Using the Fictitious Domain Method and Total - FETI Domain Decomposition

**Authors:**
Lukas Mocek,
Alexandros Markopoulos

**Abstract:**

The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

**Keywords:**
domain decomposition,
linear elasticity,
fictitious domain method,
Total-FETI,
saddle-point system

##### 21 Analytical Solution of Time-Harmonic Torsional Vibration of a Cylindrical Cavity in a Half-Space

**Authors:**
M.Eskandari-Ghadi,
M.Mahmoodian

**Abstract:**

**Keywords:**
torsion,
isotropic,
Cosine transform,
Half space,
Singular
integral equation

##### 20 Positive Solutions of Second-order Singular Differential Equations in Banach Space

**Authors:**
Li Xiguang

**Abstract:**

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

**Keywords:**
cone,
Banach space,
fixed point index,
singular equation

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

**Authors:**
Benshi Zhu

**Abstract:**

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

##### 18 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
N. Aliniya

**Abstract:**

**Keywords:**
calculus of variation,
Sinc functions,
numerical method,
galerkin