**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1991

# Search results for: New Modified Novikov Equation

##### 1991 On Symmetry Analysis and Exact Wave Solutions of New Modified Novikov Equation

**Authors:**
Anupma Bansal,
R. K. Gupta

**Abstract:**

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

**Keywords:**
New Modified Novikov Equation,
Lie Classical Method,
Nonclassical Method,
Modified (G'/G)-Expansion Method,
Traveling Wave Solutions.

##### 1990 Traveling Wave Solutions for the (3+1)-Dimensional Breaking Soliton Equation by (G'/G)- Expansion Method and Modified F-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Maliheh Najafi,
Mohammad Najafi

**Abstract:**

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

**Keywords:**
Exact solution,
The (3+1)-dimensional breaking soliton equation,
( G G )-expansion method,
Riccati equation,
Modified Fexpansion method.

##### 1989 Splitting Modified Donor-Cell Schemes for Spectral Action Balance Equation

**Authors:**
Tanapat Brikshavana,
Anirut Luadsong

**Abstract:**

**Keywords:**
donor-cell scheme,
parallel algorithm,
spectral action balance equation,
splitting method.

##### 1988 Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm

**Authors:**
S. Mousavian,
F. Mousavian,
V. Nikkhah Rashidabad

**Abstract:**

Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study show that modified equation has good agreement with experimental data.

**Keywords:**
Equation of state,
modification,
ammonia,
genetic algorithm.

##### 1987 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.

##### 1986 Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method

**Authors:**
Ou Xie,
Zhenyu Zhao

**Abstract:**

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

**Keywords:**
Ill-posed problem,
Unknown source,
Poisson equation,
Tikhonov regularization method,
Discrepancy principle

##### 1985 Modeling of Nitrogen Solubility in Stainless Steel

**Authors:**
Saeed Ghali,
Hoda El-Faramawy,
Mamdouh Eissa,
Michael Mishreky

**Abstract:**

Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacements of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600 oC: [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range.

**Keywords:**
Solubility,
nitrogen,
stainless steel,
Schaeffler.

##### 1984 New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

**Authors:**
Fadi Awawdeh,
O. Alsayyed

**Abstract:**

New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

**Keywords:**
Soliton Solution,
Hirota Bilinear Method,
ANNV System.

##### 1983 Thermodynamic Analysis of a Vapor Absorption System Using Modified Gouy-Stodola Equation

**Authors:**
Gulshan Sachdeva,
Ram Bilash

**Abstract:**

In this paper, the exergy analysis of vapor absorption refrigeration system using LiBr-H2O as working fluid is carried out with the modified Gouy-Stodola approach rather than the classical Gouy-Stodola equation and effect of varying input parameters is also studied on the performance of the system. As the modified approach uses the concept of effective temperature, the mathematical expressions for effective temperature have been formulated and calculated for each component of the system. Various constraints and equations are used to develop program in EES to solve these equations. The main aim of this analysis is to determine the performance of the system and the components having major irreversible loss. Results show that exergy destruction rate is considerable in absorber and generator followed by evaporator and condenser. There is an increase in exergy destruction in generator, absorber and condenser and decrease in the evaporator by the modified approach as compared to the conventional approach. The value of exergy determined by the modified Gouy-Stodola equation deviates maximum i.e. 26% in the generator as compared to the exergy calculated by the classical Gouy-Stodola method.

**Keywords:**
Exergy analysis,
Gouy-Stodola,
refrigeration,
vapor
absorption.

##### 1982 Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme

**Authors:**
David J. Robbins,
R. Stewart Cant,
Lynn F. Gladden

**Abstract:**

A robust AUSM+ upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of state with respect to the IAPWS-IF97 equation of state for water. The algorithm demonstrates a combination of robustness and accuracy over a range of flow conditions, with the stiffened-gas equation tending to overestimate liquid temperature and density profiles.

**Keywords:**
Multiphase flow,
AUSM+ scheme,
liquid EOS,
low Mach number models

##### 1981 Lagrangian Method for Solving Unsteady Gas Equation

**Authors:**
Amir Taghavi,
kourosh Parand,
Hosein Fani

**Abstract:**

In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

**Keywords:**
Unsteady gas equation,
Generalized Laguerre functions,
Lagrangian method,
Nonlinear ODE.

##### 1980 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.

##### 1979 Application of Modified Maxwell-Stefan Equation for Separation of Aqueous Phenol by Pervaporation

**Authors:**
Ujjal K Ghosh,
Ling Teen

**Abstract:**

Pervaporation has the potential to be an alternative to the other traditional separation processes such as distillation, adsorption, reverse osmosis and extraction. This study investigates the separation of phenol from water using a polyurethane membrane by pervaporation by applying the modified Maxwell-Stephen model. The modified Maxwell-Stefan model takes into account the non-ideal multi-component solubility effect, nonideal diffusivity of all permeating components, concentration dependent density of the membrane and diffusion coupling to predict various fluxes. Four cases has been developed to investigate the process parameters effects on the flux and weight fraction of phenol in the permeate values namely feed concentration, membrane thickness, operating temperature and operating downstream pressure. The model could describe semi-quantitatively the performance of the pervaporation membrane for the given system as a very good agreement between the observed and theoretical fluxes was observed.

**Keywords:**
Pervaporation,
Phenol,
Polyurethane,
Modified Maxwell-Stefan equation,
Solution Diffusion

##### 1978 Second-order Time Evolution Scheme for Time-dependent Neutron Transport Equation

**Authors:**
Zhenying Hong,
Guangwei Yuan,
Xuedong Fu,
Shulin Yang

**Abstract:**

In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

**Keywords:**
Exponential method,
diamond difference,
modified time discrete scheme,
second-order time evolution scheme.

##### 1977 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.

##### 1976 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.

##### 1975 The Effects of Tissue Optical Parameters and Interface Reflectivity on Light Diffusion in Biological Tissues

**Authors:**
MA. Ansari

**Abstract:**

**Keywords:**
Diffusion equation,
boundary element method,
refractive index

##### 1974 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.

##### 1973 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories

**Authors:**
Ranajay Bhowmick

**Abstract:**

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

**Keywords:**
Cubic equation,
stress invariant,
trigonometric,
explicit solution,
principal stress,
failure criterion.

##### 1972 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.

##### 1971 The Pell Equation x2 − Py2 = Q

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

**Abstract:**

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

##### 1970 Modelling an Investment Portfolio with Mandatory and Voluntary Contributions under M-CEV Model

**Authors:**
Amadi Ugwulo Chinyere,
Lewis D. Gbarayorks,
Emem N. H. Inamete

**Abstract:**

In this paper, the mandatory contribution, additional voluntary contribution (AVC) and administrative charges are merged together to determine the optimal investment strategy (OIS) for a pension plan member (PPM) in a defined contribution (DC) pension scheme under the modified constant elasticity of variance (M-CEV) model. We assume that the voluntary contribution is a stochastic process and a portfolio consisting of one risk free asset and one risky asset modeled by the M-CEV model is considered. Also, a stochastic differential equation consisting of PPM’s monthly contributions, voluntary contributions and administrative charges is obtained. More so, an optimization problem in the form of Hamilton Jacobi Bellman equation which is a nonlinear partial differential equation is obtained. Using power transformation and change of variables method, an explicit solution of the OIS and the value function are obtained under constant absolute risk averse (CARA). Furthermore, numerical simulations on the impact of some sensitive parameters on OIS were discussed extensively. Finally, our result generalizes some existing result in the literature.

**Keywords:**
DC pension fund,
modified constant elasticity of variance,
optimal investment strategies,
voluntary contribution,
administrative charges.

##### 1969 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.

##### 1968 Stability Analysis of Three-Lobe Journal Bearing Lubricated with a Micropolar Fluids

**Authors:**
Boualem Chetti

**Abstract:**

In this paper, the dynamic characteristics of a threelobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory .The finite difference technique has been used to determine the solution of the modified Reynolds equation. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show that the three-lobe bearing lubricated with micropolar fluid exhibits better stability compared with that lubricated with Newtonian fluid. According to the results obtained, the effect of the parameter micropolar fluid is remarkable on the dynamic characteristics and stability of the three-lobe bearing.

**Keywords:**
Three-lobe bearings,
Micropolar fluid,
Dynamic
characteristics,
Stability analysis.

##### 1967 An Insurer’s Investment Model with Reinsurance Strategy under the Modified Constant Elasticity of Variance Process

**Authors:**
K. N. C. Njoku,
Chinwendu Best Eleje,
Christian Chukwuemeka Nwandu

**Abstract:**

One of the problems facing most insurance companies is how best the burden of paying claims to its policy holders can be managed whenever need arises. Hence there is need for the insurer to buy a reinsurance contract in order to reduce risk which will enable the insurer to share the financial burden with the reinsurer. In this paper, the insurer’s and reinsurer’s strategy is investigated under the modified constant elasticity of variance (M-CEV) process and proportional administrative charges. The insurer considered investment in one risky asset and one risk free asset where the risky asset is modeled based on the M-CEV process which is an extension of constant elasticity of variance (CEV) process. Next, a nonlinear partial differential equation in the form of Hamilton Jacobi Bellman equation is obtained by dynamic programming approach. Using power transformation technique and variable change, the explicit solutions of the optimal investment strategy and optimal reinsurance strategy are obtained. Finally, some numerical simulations of some sensitive parameters were obtained and discussed in details where we observed that the modification factor only affects the optimal investment strategy and not the reinsurance strategy for an insurer with exponential utility function.

**Keywords:**
Reinsurance strategy,
Hamilton Jacobi Bellman equation,
power transformation,
M-CEV process,
exponential utility.

##### 1966 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

**Keywords:**
KdV equation,
Asymptotic Degeneracy,
Solitons,
Inverse Scattering

##### 1965 System Reduction Using Modified Pole Clustering and Modified Cauer Continued Fraction

**Authors:**
Jay Singh,
C. B. Vishwakarma,
Kalyan Chatterjee

**Abstract:**

A mixed method by combining modified pole clustering technique and modified cauer continued fraction is proposed for reducing the order of the large-scale dynamic systems. The denominator polynomial of the reduced order model is obtained by using modified pole clustering technique while the coefficients of the numerator are obtained by modified cauer continued fraction. This method generated 'k' number of reduced order models for kth order reduction. The superiority of the proposed method has been elaborated through numerical example taken from the literature and compared with few existing order reduction methods.

**Keywords:**
Modified Pole Clustering,
Modified Cauer
Continued Fraction,
Order Reduction,
Stability,
Transfer Function.

##### 1964 Improved Neutron Leakage Treatment on Nodal Expansion Method for PWR Reactors

**Authors:**
Antonio Carlos Marques Alvim,
Fernando Carvalho da Silva,
Aquilino Senra Martinez

**Abstract:**

**Keywords:**
Transverse leakage,
nodal expansion method,
power
density,
PWR reactors

##### 1963 Ion- Acoustic Solitary Waves in a Self- Gravitating Dusty Plasma Having Two-Temperature Electrons

**Authors:**
S.N.Paul,
G.Pakira,
B.Paul,
B.Ghosh

**Abstract:**

**Keywords:**
Charge fluctuations,
gravitating dusty plasma,
Ionacoustic
solitary wave,
Two-temperature electrons

##### 1962 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.