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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Numerical Solution of A System of Singularly Perturbed Convection-Diffusion Boundary-Value Problems Using Mesh Equidistribution Technique
Author(s):
Pratibhamoy Das and Srinivasan Natesan
Department of Mathematics,
Indian Institute of Technology Guwahati,
Guwahati - 781 039,
India.
pratibhamoy@gmail.com
natesan@iitg.ernet.in
URL:
http://www.iitg.ernet.in/natesan/
Abstract:
In this article, we consider a system of singularly perturbed weakly coupled convection-diffusion equations having diffusion parameters of different magnitudes. These small parameters give rise to boundary layers. An upwind finite difference scheme on adaptively generated mesh is used to obtain a suitable monitor function that gives first-order convergence which is robust with respect to the diffusion parameters. We present the results of numerical experiments for linear and semilinear system of differential equations to support the effectiveness of our preferred monitor function obtained from theoretical analysis.
Paper's Title:
Fractional class of analytic functions Defined Using q-Differential Operator
Author(s):
K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan
Department of Mathematics and
Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
E-mail: kr_karthikeyan1979@yahoo.com
College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
E-mail: musthafa.ibrahim@gmail.com
Department of Mathematics, Presidency
College (Autonomous),
Chennai-600005, Tamilnadu,
India.
Abstract:
We define a q-differential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving q-differential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.
Paper's Title:
(p,q)-Lucas Polynomial and Their Applications to a Certain Family of Bi-univalent Functions Defined by Wanas Operator
Author(s):
M Musthafa Ibrahim, Saleem Ahmed
College of Engineering
University of Buraimi
Al Buraimi, P.O.Box 512,
Oman
E-mail: musthafa.i@uob.edu.om,
saleem.a@uob.edu.om
Abstract:
In this article, by making use of (p,q)-Lucas polynomials, we introduce and investigate a certain family of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk U. Also, the upper bounds for the initial Taylor-Maclaurin coefficients and the Fekete-Szegö inequality of functions belonging to this family are obtained.
Paper's Title:
Oscillation Criteria for Second Order Delay Difference Equations via Canonical Transformations and Some New Monotonic Properties
Author(s):
R. Deepalakhmi, S. Saravanan, J. R. Graef, and E. Thandapani
Department of Interdisciplinary Studies
Tamil Nadu Dr. Ambedkar Law University
Chennai-600113,
India.
profdeepalakshmi@gmail.com
Madras School of Economics,
Chennai-600025,
India.
profsaran11@gmail.com
Department of Mathematics,
University of Tennessee at Chattanooga,
Chattanooga,TN 37403,
USA.
john-graef@utc.edu
Ramanujan Institute for Advanced Study in
Mathematics,
University of Madras,
Chennai - 600 005,
India.
ethandapani@yahoo.co.in
Abstract:
This paper is concerned with second-order linear noncanonical delay difference equations of the form
Δ(μ(t)Δ y(t))+ p(t)y(φ(t))=0.
The authors prove new oscillation criteria by first transforming the equation into canonical form and then obtaining some new monotonic properties of the positive solutions of the transformed equation. By using a comparison with first-order delay difference equations and a generalization of a technique developed by Koplatadze, they obtain their main results. Examples illustrating the improvement over known results in the literature are presented.
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