**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1629

# Search results for: Pseudo-hyperbolic partial integro-differential equations

##### 1629 A Nonconforming Mixed Finite Element Method for Semilinear Pseudo-Hyperbolic Partial Integro-Differential Equations

**Authors:**
Jingbo Yang,
Hong Li,
Yang Liu,
Siriguleng He

**Abstract:**

In this paper, a nonconforming mixed finite element method is studied for semilinear pseudo-hyperbolic partial integrodifferential equations. By use of the interpolation technique instead of the generalized elliptic projection, the optimal error estimates of the corresponding unknown function are given.

**Keywords:**
Pseudo-hyperbolic partial integro-differential equations,
Nonconforming mixed element method,
Semilinear,
Error
estimates.

##### 1628 A New Splitting H1-Galerkin Mixed Method for Pseudo-hyperbolic Equations

**Authors:**
Yang Liu,
Jinfeng Wang,
Hong Li,
Wei Gao,
Siriguleng He

**Abstract:**

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

**Keywords:**
Pseudo-hyperbolic equations,
splitting system,
H1-Galerkin mixed method,
error estimates.

##### 1627 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.

##### 1626 Exp-Function Method for Finding Some Exact Solutions of Rosenau Kawahara and Rosenau Korteweg-de Vries Equations

**Authors:**
Ehsan Mahdavi

**Abstract:**

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

**Keywords:**
Exp-function method,
Rosenau Kawahara equation,
Rosenau Korteweg-de Vries equation,
nonlinear partial differential
equation.

##### 1625 Pricing European Options under Jump Diffusion Models with Fast L-stable Padé Scheme

**Authors:**
Salah Alrabeei,
Mohammad Yousuf

**Abstract:**

**Keywords:**
Integral differential equations,
L-stable methods,
pricing European options,
Jump–diffusion model.

##### 1624 An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon

**Authors:**
Haniye Dehestani,
Yadollah Ordokhani

**Abstract:**

**Keywords:**
Collocation method,
fractional partial differential
equations,
Legendre-Laguerre functions,
pseudo-operational matrix
of integration.

##### 1623 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

**Keywords:**
Electromagnetism,
Maxwell's Equations,
Anisotropic permittivity,
Wave equation,
Matrix Equation,
Permittivity tensor.

##### 1622 Adomian Decomposition Method Associated with Boole-s Integration Rule for Goursat Problem

**Authors:**
Mohd Agos Salim Nasir,
Ros Fadilah Deraman,
Siti Salmah Yasiran

**Abstract:**

**Keywords:**
Goursat problem,
partial differential equation,
Adomian decomposition method,
Boole's integration rule.

##### 1621 Numerical Study of a Class of Nonlinear Partial Differential Equations

**Authors:**
Kholod M. Abu-Alnaja

**Abstract:**

**Keywords:**
Crank-Nicolson Scheme,
Douglas Scheme,
Partial
Differential Equations

##### 1620 Solving SPDEs by a Least Squares Method

**Authors:**
Hassan Manouzi

**Abstract:**

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

**Keywords:**
Least squares,
Wick product,
SPDEs,
finite element,
Wiener chaos expansion,
gradient method.

##### 1619 The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
T. Danjuma

**Abstract:**

An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

**Keywords:**
Option price valuation,
Partial Differential Equations,
Black-Scholes PDEs,
Ito process.

##### 1618 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.

##### 1617 A Fully Implicit Finite-Difference Solution to One Dimensional Coupled Nonlinear Burgers’ Equations

**Authors:**
Vineet K. Srivastava,
Mukesh K. Awasthi,
Mohammad Tamsir

**Abstract:**

A fully implicit finite-difference method has been proposed for the numerical solutions of one dimensional coupled nonlinear Burgers’ equations on the uniform mesh points. The method forms a system of nonlinear difference equations which is to be solved at each iteration. Newton’s iterative method has been implemented to solve this nonlinear assembled system of equations. The linear system has been solved by Gauss elimination method with partial pivoting algorithm at each iteration of Newton’s method. Three test examples have been carried out to illustrate the accuracy of the method. Computed solutions obtained by proposed scheme have been compared with analytical solutions and those already available in the literature by finding L2 and L∞ errors.

**Keywords:**
Burgers’ equation,
Implicit Finite-difference method,
Newton’s method,
Gauss elimination with partial pivoting.

##### 1616 On Symmetries and Exact Solutions of Einstein Vacuum Equations for Axially Symmetric Gravitational Fields

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

**Abstract:**

**Keywords:**
Gravitational fields,
Lie Classical method,
Exact solutions.

##### 1615 Numerical Investigation of Two-dimensional Boundary Layer Flow Over a Moving Surface

**Authors:**
Mahmoud Zarrini,
R.N. Pralhad

**Abstract:**

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

**Keywords:**
Boundary layer,
continuously moving surface,
shooting method,
skin friction coefficient.

##### 1614 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev

**Abstract:**

**Keywords:**
Homotopy perturbation method,
Padé approximants,
cubic Boussinesq equation,
modified Boussinesq equation.

##### 1613 Tracking Control of a Linear Parabolic PDE with In-domain Point Actuators

**Authors:**
Amir Badkoubeh,
Guchuan Zhu

**Abstract:**

**Keywords:**
Tracking Control,
In-domain point actuation,
PartialDifferential Equations.

##### 1612 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method

**Authors:**
Kourosh Parand,
Jamal Amani Rad

**Abstract:**

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

**Keywords:**
Exp-function method,
generalized Pochhammer- Chree equation,
solitary wave solution,
ODE's.

##### 1611 Applications of High-Order Compact Finite Difference Scheme to Nonlinear Goursat Problems

**Authors:**
Mohd Agos Salim Nasir,
Ahmad Izani Md. Ismail

**Abstract:**

**Keywords:**
Goursat problem,
partial differential equation,
finite
difference scheme,
compact finite difference

##### 1610 The Proof of Analogous Results for Martingales and Partial Differential Equations Options Price Valuation Formulas Using Stochastic Differential Equation Models in Finance

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
A. H. Usman

**Abstract:**

Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

**Keywords:**
Option price valuation,
Martingales,
Partial Differential Equations,
PDEs,
Equivalent Martingale Measure,
Girsanov Theorem,
Feyman-Kac Theorem,
European Put Option.

##### 1609 Exact Pfaffian and N-Soliton Solutions to a (3+1)-Dimensional Generalized Integrable Nonlinear Partial Differential Equations

**Authors:**
Magdy G. Asaad

**Abstract:**

**Keywords:**
Bilinear operator,
G-BKP equation,
Integrable nonlinear PDEs,
Jimbo-Miwa equation,
Ma-Fan equation,
N-soliton solutions,
Pfaffian solutions.

##### 1608 On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid

**Authors:**
A. Giniatoulline

**Abstract:**

**Keywords:**
Galerkin method,
Navier-Stokes equations,
nonlinear partial differential equations,
Sobolev spaces,
stratified fluid.

##### 1607 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation

**Authors:**
Anupma Bansal

**Abstract:**

We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.

**Keywords:**
Klein-Gordon-Schödinger Equation,
Lie Classical Method,
Exact Solutions

##### 1606 Thermophoretic Deposition of Nanoparticles Due Toa Permeable Rotating Disk: Effects of Partial Slip, Magnetic Field, Thermal Radiation, Thermal-Diffusion, and Diffusion-Thermo

**Authors:**
M. M. Rahman

**Abstract:**

**Keywords:**
Boundary layer flows,
convection,
diffusion-thermo,
rotating disk,
thermal-diffusion,
thermophoresis.

##### 1605 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.

##### 1604 Dynamic Modeling and Simulation of Heavy Paraffin Dehydrogenation Reactor for Selective Olefin Production in Linear Alkyl Benzene Production Plant

**Authors:**
G. Zahedi,
H. Yaghoobi

**Abstract:**

**Keywords:**
Dehydrogenation,
fixed bed reactor,
modeling,
linear alkyl benzene.

##### 1603 Study of MHD Oblique Stagnation Point Assisting Flow on Vertical Plate with Uniform Surface Heat Flux

**Authors:**
Phool Singh,
Ashok Jangid,
N.S. Tomer,
Deepa Sinha

**Abstract:**

**Keywords:**
Heat flux,
Oblique stagnation point,
Mixedconvection,
Magneto hydrodynamics

##### 1602 Rear Separation in a Rotating Fluid at Moderate Taylor Numbers

**Authors:**
S. Damodaran,
T. V. S.Sekhar

**Abstract:**

**Keywords:**
Navier_Stokes equations,
Taylor number,
Reynolds number,
Higher order compact scheme,
Rotating Fluid.

##### 1601 A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces

**Authors:**
Mei-Hsiu Chi,
Jyh-Yang Wu,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Close surfaces,
high-order approach,
numerical solutions,
reaction-diffusion systems.

##### 1600 A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation

**Authors:**
Vikas Tewari,
K.R. Pardasani

**Abstract:**

**Keywords:**
rapid buffer approximation,
sodium-calcium exchangeprotein,
Sarcolemmal Calcium ATPase pump,
buffer disassociationrate,
forward time centred space.