**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**371

# Search results for: Laplace’s equation

##### 371 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.

##### 370 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.

##### 369 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.

##### 368 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.

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

**Abstract:**

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

##### 366 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

##### 365 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.

##### 364 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.

##### 363 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.

##### 362 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.

##### 361 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

##### 360 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.

##### 359 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.

##### 358 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.

##### 357 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.

##### 356 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.

##### 355 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.

##### 354 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,
Lane-Emden equation,
Riemann-Liouville fractional operators,
Volterra integral equation.

##### 353 Existence of Iterative Cauchy Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

**Keywords:**
Fractional calculus,
fractional differential equation,
Cauchy equation,
Riemann-Liouville fractional operators,
Volterra
integral equation,
non-expansive mapping,
iterative differential equation.

##### 352 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.

##### 351 The Diophantine Equation y2 − 2yx − 3 = 0 and Corresponding Curves over Fp

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Hatice Alkan

**Abstract:**

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

##### 350 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.

##### 349 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.

##### 348 The Pell Equation x2 − Py2 = Q

**Authors:**
Ahmet Tekcan,
Arzu Özkoç,
Canan Kocapınar,
Hatice Alkan

**Abstract:**

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

##### 347 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.

##### 346 Evolutionary Computation Technique for Solving Riccati Differential Equation of Arbitrary Order

**Authors:**
Raja Muhammad Asif Zahoor,
Junaid Ali Khan,
I. M. Qureshi

**Abstract:**

**Keywords:**
Riccati Equation,
Non linear ODE,
Fractional differential equation,
Genetic algorithm.

##### 345 Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method

**Authors:**
Nisha Goyal,
R.K. Gupta

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

**Keywords:**
Sawada-Kotera-Kadomtsev-Petviashivili equation,
Bogoyavlensky-Konoplechenko equation,

##### 344 Performances Analysis of the Pressure and Production of an Oil Zone by Simulation of the Flow of a Fluid through the Porous Media

**Authors:**
Makhlouf Mourad,
Medkour Mihoub,
Bouchher Omar,
Messabih Sidi Mohamed,
Benrachedi Khaled

**Abstract:**

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

**Keywords:**
Darcy equation,
middle porous,
continuity equation,
Peng Robinson equation,
mobility.

##### 343 The Pell Equation x2 − (k2 − k)y2 = 2t

**Authors:**
Ahmet Tekcan

**Abstract:**

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

##### 342 Lagrange-s Inversion Theorem and Infiltration

**Authors:**
Pushpa N. Rathie,
Prabhata K. Swamee,
André L. B. Cavalcante,
Luan Carlos de S. M. Ozelim

**Abstract:**

**Keywords:**
Green-Ampt Equation,
Lagrange's Inversion
Theorem,
Talsma-Parlange Equation,
Three-Parameter Infiltration
Equation