**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1112

# Search results for: Laplace’s equation

##### 1112 A Modified Laplace Decomposition Algorithm Solution for Blasius’ Boundary Layer Equation of the Flat Plate in a Uniform Stream

**Authors:**
M. A. Koroma,
Z. Chuangyi,
A. F.,
Kamara,
A. M. H. Conteh

**Abstract:**

In this work, we apply the Modified Laplace decomposition algorithm in finding a numerical solution of Blasius’ boundary layer equation for the flat plate in a uniform stream. The series solution is found by first applying the Laplace transform to the differential equation and then decomposing the nonlinear term by the use of Adomian polynomials. The resulting series, which is exactly the same as that obtained by Weyl 1942a, was expressed as a rational function by the use of diagonal padé approximant.

**Keywords:**
Modified Laplace decomposition algorithm,
Boundary
layer equation,
Padé approximant,
Numerical solution.

##### 1111 Laplace Technique to Find General Solution of Differential Equations without Initial Conditions

**Authors:**
Adil Al-Rammahi

**Abstract:**

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

**Keywords:**
Differential Equations,
Laplace Transformations.

##### 1110 A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions

**Authors:**
Khaled Moaddy

**Abstract:**

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

**Keywords:**
Standard finite difference schemes,
non–standard schemes,
Laplace equation,
Dirichlet boundary conditions.

##### 1109 On Method of Fundamental Solution for Nondestructive Testing

**Abstract:**

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

##### 1108 Stability Analysis of Linear Fractional Order Neutral System with Multiple Delays by Algebraic Approach

**Authors:**
Lianglin Xiong,
Yun Zhao,
Tao Jiang

**Abstract:**

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

**Keywords:**
Fractional neutral differential equation,
Laplace transform,
characteristic equation.

##### 1107 Stability Analysis in a Fractional Order Delayed Predator-Prey Model

**Authors:**
Changjin Xu,
Peiluan Li

**Abstract:**

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

**Keywords:**
Fractional predator-prey model,
laplace transform,
characteristic equation.

##### 1106 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
Chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series.

##### 1105 Autonomous Vehicle Navigation Using Harmonic Functions via Modified Arithmetic Mean Iterative Method

**Authors:**
Azali Saudi,
Jumat Sulaiman

**Abstract:**

**Keywords:**
Modified Arithmetic Mean method,
Harmonic
functions,
Laplace’s equation,
path planning.

##### 1104 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.

##### 1103 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.

##### 1102 Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method

**Authors:**
Said Laachir,
Aziz Laaribi

**Abstract:**

The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

**Keywords:**
Helmholtz equation,
Nikiforov-Uvarov method,
exact solutions,
eigenfunctions.

##### 1101 Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method

**Authors:**
Changqing Yang,
Jianhua Hou

**Abstract:**

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

**Keywords:**
Integro-differential equations,
Laplace transform,
fractional derivative,
adomian polynomials,
pade appoximants.

##### 1100 The Boundary Element Method in Excel for Teaching Vector Calculus and Simulation

**Authors:**
Stephen Kirkup

**Abstract:**

**Keywords:**
Boundary element method,
laplace equation,
vector calculus,
simulation,
education.

##### 1099 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.

##### 1098 Transient Currents in a Double Conductor Line above a Conducting Half-Space

**Authors:**
Valentina Koliskina,
Inta Volodko

**Abstract:**

**Keywords:**
Transient eddy currents,
Laplace transform,
double
conductor line.

##### 1097 Laplace Adomian Decomposition Method Applied to a Two-Dimensional Viscous Flow with Shrinking Sheet

**Authors:**
M. A. Koroma,
S. Widatalla,
A. F. Kamara,
C. Zhang

**Abstract:**

**Keywords:**
Adomian polynomials,
Laplace Adomian
decomposition method,
Padé Approximant,
Shrinking sheet.

##### 1096 Dynamic Response of Nano Spherical Shell Subjected to Termo-Mechanical Shock Using Nonlocal Elasticity Theory

**Authors:**
J. Ranjbarn,
A. Alibeigloo

**Abstract:**

**Keywords:**
Nano-scale spherical shell,
nonlocal elasticity
theory,
thermomechanical shock.

##### 1095 Laplace Transformation on Ordered Linear Space of Generalized Functions

**Authors:**
K. V. Geetha,
N. R. Mangalambal

**Abstract:**

**Keywords:**
Laplace transformable generalized function,
positive cone,
topology of bounded convergence

##### 1094 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

**Authors:**
Lv Yuhua

**Abstract:**

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

**Keywords:**
Cone,
fixed point index,
eigenvalue problem,
p-Laplace operator,
positive solutions.

##### 1093 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

**Authors:**
M. A. Koroma,
C. Zhan,
A. F. Kamara,
A. B. Sesay

**Abstract:**

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

**Keywords:**
Laplace decomposition,
pantograph equations,
exact
solution,
numerical solution,
approximate solution.

##### 1092 Generalized Stokes’ Problems for an Incompressible Couple Stress Fluid

**Authors:**
M.Devakar,
T.K.V.Iyengar

**Abstract:**

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

**Keywords:**
Couple stress fluid,
Generalized Stokes’ problems,
Laplace transform,
Numerical inversion

##### 1091 Three-Dimensional Generalized Thermoelasticity with Variable Thermal Conductivity

**Authors:**
Hamdy M. Youssef,
Mowffaq Oreijah,
Hunaydi S. Alsharif

**Abstract:**

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

**Keywords:**
Thermoelasticity,
three-dimensional,
Laplace transforms,
Fourier transforms,
thermal conductivity.

##### 1090 On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section

**Authors:**
A.Campanile,
M. Mandarino,
V. Piscopo,
A. Pranzitelli

**Abstract:**

**Keywords:**
Non-uniform torsion,
Axial symmetric cross-section,
Fourier series,
Helmholtz equation,
FE method.

##### 1089 On the Integer Solutions of the Pell Equation x2 - dy2 = 2t

**Authors:**
Ahmet Tekcan,
Betül Gezer,
Osman Bizim

**Abstract:**

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

**Keywords:**
Pell equation,
Diophantine equation.

##### 1088 Dynamics of a Vapour Bubble inside a Vertical Rigid Cylinder in the Absence of Buoyancy Forces

**Authors:**
S. Mehran,
S. Rouhi,
F.Rouzbahani,
E. Haghgoo

**Abstract:**

**Keywords:**
Vapour bubble,
Vertical rigid cylinder,
Boundaryelement method,
Finite difference method,
Buoyancy forces.

##### 1087 Action Functional of the Electomagnetic Field: Effect of Gravitation

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

**Keywords:**
General theory of relativity,
electromagnetism,
metric tensor,
Maxwells equations,
test functions,
finite element method.

##### 1086 The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

**Authors:**
Armend Sh. Shabani

**Abstract:**

**Keywords:**
Pell's equation,
solutions of Pell's equation.

##### 1085 Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam

**Authors:**
Geeta Partap,
Nitika Chugh

**Abstract:**

**Keywords:**
Microstretch,
deflection,
exponential load,
Laplace
transforms,
Residue theorem,
simply supported.

##### 1084 Transient Heat Transfer of a Spiral Fin

**Authors:**
Sen-Yung Lee,
Li-Kuo Chou,
Chao-Kuang Chen

**Abstract:**

**Keywords:**
Laplace transforms/Adomian decomposed method- Padé,
transient response,
heat transfer.

##### 1083 An Analytical Method for Solving General Riccati Equation

**Authors:**
Y. Pala,
M. O. Ertas

**Abstract:**

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

**Keywords:**
Riccati Equation,
ordinary differential equation,
nonlinear differential equation,
analytical solution,
proper solution.