|
On a New Solution for the Viscoelastic Squeezing Flow between Two Parallel Plates
|
|
Zodwa Makukula, Sandile Motsa, Precious Sibanda
|
|
Volume 2, Issue 4, 2010
pp.
31 - 38
|
|
Received
03 June 2010,
Accepted
26 July 2010
|
|
Abstract.
A newly developed successive linearization method for nonlinear problems in engineering and science is used to solve the nonlinear equation governing two-dimensional constant speed squeezing flow of a viscous fluid between two approaching parallel plates. The results obtained using the SLM were compared with those in the literature and against the numerical solution in terms of accuracy and efficiency of the method. The findings from the comparisons prove that the SLM is powerful, more efficient yet simple to use than the HAM and is independent of the size of parameter values used in the problem.
|
|
Keywords.
Squeezing flow; Linearization method; Spectral method;
Nonlinear equations
|
|
Full Text:
PDF
|
|
|
Improving Homotopy Analysis Method for System of Nonlinear Equations
|
|
M.M. Hosseini, S.M. Hosseini
|
|
Volume 2, Issue 4, 2010
pp.
22 - 30
|
|
Received
13 February 2010,
Accepted
06 July 2010
|
|
Abstract.
In this paper, a new iterative method for solving the system of nonlinear equations is suggested based on Newton-Raphson method and homotopy analysis method. Comparison of the result obtained by present method with Newton-Raphson method and homotopy perturbation method reveals that the accuracy and fast convergence of the proposed method.
|
|
Keywords.
Homotopy analysis method;
System of nonlinear equations;
Newton-Raphson method.
|
|
Full Text:
PDF
|
|
|
Application of Variational Iteration Method to Solve a Degenerate Convection-Diffusion Equation Arising in Flow in Porous Media
|
|
V. Soti
|
|
Volume 2, Issue 4, 2010
pp.
14 - 21
|
|
Received
09 March 2010,
Accepted
29 June 2010
|
|
Abstract.
In this paper a nonlinear degenerate convection-diffusion problem describing two-phase flow in porous media is considered in petroleum reservoir and groundwater aquifer. A weighted algorithm based on variational iteration method is used to solve this nonlinear degenerate, convection-diffusion problem. For illustration purpose, two test problems are considered and their approximate and exact solutions are compared.
|
|
Keywords.
Petroleum reservoirs; Porous media; Diffusion equation; Variational iteration method.
|
|
Full Text:
PDF
|
|
|
On Schur Diagonal Stability
|
|
Handan Akyar
|
|
Volume 2, Issue 4, 2010
pp.
1 - 13
|
|
Received
19 April 2010,
Accepted
27 June 2010
|
|
Abstract.
In this paper, a necessary and sufficient condition which ensures the existence of diagonal solution of the Stein inequality for a $2\times 2$ matrix is given. Then, this result is extended to common diagonal solution of finite number of $2\times 2$ matrices. Schur diagonal stability of segment of matrices is also considered. Furthermore, a sufficient condition is obtained for Schur diagonal stability of $3\times 3$ matrices. Some explanatory examples are presented in the text.
|
|
Keywords.
Schur diagonal stability; Hurwitz diagonal stability; Stein inequality.
|
|
Full Text:
PDF
|
|
|
Approximation of Solutions of a Generalized System of Variational Inclusions
|
|
S.Y. Cho, C.Q. Wu, Y. Li
|
|
Volume 2, Issue 3, 2010
pp.
73 - 82
|
|
Received
22 April 2010,
Accepted
11 June 2010
|
|
Abstract.
In this paper, we introduce a generalized system of nonlinear relaxed cocoercive variational inclusions involving (A,\eta)-monotone mappings in the framework of real Hilbert spaces. Based on the generalized resolvent operator technique associated with (A,\eta)-monotonicity, we consider the approximation solvability of solutions.
|
|
Keywords.
(A,\eta)-monotone mapping; Nonexpansive mappings; A-monotone mappings; H-monotone mappings; Hilbert space.
|
|
Full Text:
PDF
|
|
|
On Totally \delta-Precontinuous Functions
|
|
C. Carpintero, N. Rajesh, E. Rosas
|
|
Volume 2, Issue 3, 2010
pp.
64 - 72
|
|
Received
13 March 2010,
Accepted
07 June 2010
|
|
Abstract.
In this paper, \delta-preopen sets and \delta-preclosed sets are used to define and investigate a new class of functions called, totally \delta-precontinuous functions. Relationships between this new class and other classes of related functions are established.
|
|
Keywords.
Topological spaces; \delta-preopen sets; Totally \delta-precontinuous functions.
|
|
Full Text:
PDF
|
|
|
On the Generalization of the Standard SIR Model of Infectious Diseases and its HAM Solution
|
|
Precious Sibanda, Sandile Motsa, Zodwa Makukula
|
|
Volume 2, Issue 3, 2010
pp.
47 - 63
|
|
Received
04 February 2010,
Accepted
24 May 2010
|
|
Abstract.
In this paper, a general model system of equations for the standard SIR epidemic models for simulating the spread of infectious diseases is formulated and its solution is determined using the Homotopy Analysis Method (HAM). The system fits all autonomous SIR epidemic models involving the three classes, susceptibles (S(t)), infectious (I(t)), and the recovered/removed (R(t)). Illustrative examples are then used to verify the validity of the analytical solution, and further compared with the classical fourth-order Runge-Kutta schemes, which reveals the power of the HAM as a tool for solving nonlinear systems of ODEs.
|
|
Keywords.
SIR epidemic models; Homotopy analysis method (HAM).
|
|
Full Text:
PDF
|
|
|
Generalized Topology of an Enlargement
|
|
V. Renukadevi
|
|
Volume 2, Issue 3, 2010
pp.
38 - 46
|
|
Received
05 April 2010,
Accepted
18 May 2010
|
|
Abstract.
We prove that the family of all $\kappa-$open sets of a regular enlargement $\kappa$ defined on a generalized topology is a quasi-topology and prove that almost all identities involving the closure and interior operators in any topological space are valid for the closure and interior operators of this quasi-topology.
|
|
Keywords.
$\mu-$enlargment; Generalized open sets; Generalized topology; Quasi-topology; $\lambda-$friendly functions; Operations.
|
|
Full Text:
PDF
|
|
|
Analysis of the Synthesis of Biodiesel Using the Homotopy Analysis Method
|
|
Precious Sibanda, Sandile Motsa, Zodwa Makukula
|
|
Volume 2, Issue 3, 2010
pp.
23 - 37
|
|
Received
25 February 2010,
Accepted
14 May 2010
|
|
Abstract.
Commercial and industrial companies generally strive to increase production and offer affordable quality products through on-going research and innovation. Mathematical modeling and simulation is a vital tool in any research to optimize product development at minimum cost. In this paper we present a mathematical model for the synthesis of biodiesel from vegetable oils and animal fats. An analytical series solution of the model equations is obtained using the homotopy analysis method (HAM). The accuracy of the analytic result is validated by comparison with known experimental results and numerical results obtained using a forth-order Runge-Kutta technique. The effect of the reaction rate constants on the transesterification process is also investigated.
|
|
Keywords.
Biodiesel; Homotopy analysis method; Mathematical model; Series solution.
|
|
Full Text:
PDF
|
|
|
On Weak Separation Axioms via (1, 2)*-Semi-Generalized Closed Sets
|
|
Nirmala Mariappan, E. Hatir, M. Lellis Thivagar
|
|
Volume 2, Issue 3, 2010
pp.
13 - 22
|
|
Received
01 February 2010,
Accepted
09 May 2010
|
|
Abstract.
The aim of this paper is to introduce and study two new classes of bitopological spaces called (1,2)*-semi-g-regular and (1,2)*-semi-g- normal spaces. (1,2)*-semi-g-regularity and (1,2)*-semi-g-normality are separation properties obtained by utilizing (1,2)*-semi-generalized closed sets.
|
|
Keywords.
(1,2)*-semi-open sets; (1,2)*-semi-generalized
closed sets; (1,2)*-semi-g-regular space;(1,2)*-semi-g-normal space.
|
|
Full Text:
PDF
|
|