**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3059

# Search results for: boundary value problems

##### 3059 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.

##### 3058 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.

##### 3057 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.

##### 3056 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.

##### 3055 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.

##### 3054 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:**
The couple-stress thermo-elasticity,
boundary value problems.

##### 3053 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

##### 3052 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

##### 3051 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

##### 3050 Positive Solutions for a Class of Semipositone Discrete Boundary Value Problems with Two Parameters

**Authors:**
Benshi Zhu

**Abstract:**

**Keywords:**
Discrete boundary value problems,
nonsmoothcritical point theory,
positive solutions,
semipositone,
sub-super solutions method

##### 3049 Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

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

**Abstract:**

**Keywords:**
trigonometric B-spline,
two-point boundary valueproblem,
spline interpolation,
cubic spline

##### 3048 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

##### 3047 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

**Authors:**
Jalil Rashidinia,
Reza Jalilian

**Abstract:**

**Keywords:**
Quintic non-polynomial spline,
Boundary formula,
Convergence,
Obstacle problems.

##### 3046 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.

##### 3045 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.

##### 3044 Haar wavelet Method for Solving Initial and Boundary Value Problems of Bratu-type

**Authors:**
S.G.Venkatesh,
S.K.Ayyaswamy,
G.Hariharan

**Abstract:**

In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

**Keywords:**
Haar wavelet method,
Bratu's problem,
boundary value problems,
initial value problems,
adomain decomposition method.

##### 3043 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.

##### 3042 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.

##### 3041 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.

##### 3040 A Laplace Transform Dual-Reciprocity Boundary Element Method for Axisymmetric Elastodynamic Problems

**Authors:**
B. I. Yun

**Abstract:**

**Keywords:**
Axisymmetric elasticity,
boundary element method,
dual-reciprocity method,
Laplace transform.

##### 3039 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:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 3038 Sinc-Galerkin Method for the Solution of Problems in Calculus of Variations

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

**Abstract:**

**Keywords:**
Calculus of variation; Sinc functions; Galerkin; Numerical method

##### 3037 Non-Polynomial Spline Method for the Solution of Problems in Calculus of Variations

**Authors:**
M. Zarebnia,
M. Hoshyar,
M. Sedaghati

**Abstract:**

**Keywords:**
Calculus of variation; Non-polynomial spline functions; Numerical method

##### 3036 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:**
Banach space,
cone,
fixed point index,
singular differential
equation,
p-Laplace operator,
symmetric solutions.

##### 3035 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.

##### 3034 Application of Higher Order Splines for Boundary Value Problems

**Authors:**
Pankaj Kumar Srivastava

**Abstract:**

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

##### 3033 A Meshfree Solution of Tow-Dimensional Potential Flow Problems

**Authors:**
I. V. Singh,
A. Singh

**Abstract:**

In this paper, mesh-free element free Galerkin (EFG) method is extended to solve two-dimensional potential flow problems. Two ideal fluid flow problems (i.e. flow over a rigid cylinder and flow over a sphere) have been formulated using variational approach. Penalty and Lagrange multiplier techniques have been utilized for the enforcement of essential boundary conditions. Four point Gauss quadrature have been used for the integration on two-dimensional domain (Ω) and nodal integration scheme has been used to enforce the essential boundary conditions on the edges (┌). The results obtained by EFG method are compared with those obtained by finite element method. The effects of scaling and penalty parameters on EFG results have also been discussed in detail.

**Keywords:**
Meshless,
EFG method,
potential flow,
Lagrange multiplier method,
penalty method,
penalty parameter and scaling parameter

##### 3032 Inverse Heat Conduction Analysis of Cooling on Run Out Tables

**Authors:**
M. S. Gadala,
Khaled Ahmed,
Elasadig Mahdi

**Abstract:**

In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

**Keywords:**
Inverse Analysis,
Function Specification,
Neural Net
Works,
Particle Swarm,
Run Out Table.

##### 3031 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.

##### 3030 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.