**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**25

# Search results for: Laplace

##### 25 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

##### 24 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.

##### 23 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.

##### 22 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.

##### 21 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.

##### 20 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.

##### 19 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.

##### 18 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.

##### 17 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.

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

**Abstract:**

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

##### 15 Capture Zone of a Well Field in an Aquifer Bounded by Two Parallel Streams

**Authors:**
S. Nagheli,
N. Samani,
D. A. Barry

**Abstract:**

**Keywords:**
Complex potential,
conformal mapping,
groundwater remediation,
image well theory,
Laplace’s equation,
superposition principle.

##### 14 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.

##### 13 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.

##### 12 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.

##### 11 Closed Form Solution to problem of Calcium Diffusion in Cylindrical Shaped Neuron Cell

**Authors:**
Amrita Tripathi,
Neeru Adlakha

**Abstract:**

**Keywords:**
Laplace Transform,
Modified Bessel function,
reaction diffusion equation,
diffusion coefficient,
excess buffer,
calcium influx

##### 10 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.

##### 9 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.

##### 8 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.

##### 7 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.

##### 6 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.

##### 5 Dynamic Analysis of Viscoelastic Plates with Variable Thickness

**Authors:**
Gülçin Tekin,
Fethi Kadıoğlu

**Abstract:**

In this study, the dynamic analysis of viscoelastic plates with variable thickness is examined. The solutions of dynamic response of viscoelastic thin plates with variable thickness have been obtained by using the functional analysis method in the conjunction with the Gâteaux differential. The four-node serendipity element with four degrees of freedom such as deflection, bending, and twisting moments at each node is used. Additionally, boundary condition terms are included in the functional by using a systematic way. In viscoelastic modeling, Three-parameter Kelvin solid model is employed. The solutions obtained in the Laplace-Carson domain are transformed to the real time domain by using MDOP, Dubner & Abate, and Durbin inverse transform techniques. To test the performance of the proposed mixed finite element formulation, numerical examples are treated.

**Keywords:**
Dynamic analysis,
inverse Laplace transform techniques,
mixed finite element formulation,
viscoelastic plate with variable thickness.

##### 4 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.

##### 3 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.

##### 2 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

##### 1 Variational EM Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

**Keywords:**
Bayesian rule,
Gaussian process classification model
with multiclass,
Gaussian process prior,
human action classification,
laplace approximation,
variational EM algorithm.