Paper's Title:

Robust Layer Resolving Scheme for a System of Two Singularly Perturbed Time-Dependent Delay Initial Value Problems with Robin Initial Conditions

Author(s):

¹K. Ramiya Bharathi, ²G. E. Chatzarakis, ²S. L. Panetsos, and ¹M. Joseph Paramasivam

¹PG & Research Department of Mathematics,
Bishop Heber College (Affiliated to Bharathidasan University),
Tiruchirappalli - 620 017, Tamil Nadu,
India.
E-mail: ramiyabharathik28@gmail.com, paramasivam.ma@bhc.edu.i 

²Department of Electrical and Electronic Engineering Educators,
School of Pedagogical \& Technological Education (ASPETE),
Marousi, 15122, Athens,
Greece.
E-mail: gea.xatz@aspete.gr, spanetsos@aspete.gr

Abstract:

This paper aimed at proving first order convergence for system of two singularly perturbed time-dependent initial value problems with delay in spatial variable and robin initial conditions. A Classical layer resolving finite difference scheme is developed by implementing uniform mesh for time discretization; Shishkin-mesh, a piecewise uniform mesh for spatial discretization. Shishkin-mesh is constructed is such way it captures the intricacies behavior of the layers. The interior layer is induced by the presence of a delay term in the space term. Error estimate is carried out to prove first order convergence with the help of maximum principle, stability analysis, solution bounds and sharper estimates of the singular components of the solutions. Finally, the numerical illustration is computed for the problem to bolster the scheme.

Paper's Title:

Coefficient Estimates for Certain Subclasses of Bi-univalent Sakaguchi Type Functions by using Faber Polynomial

Author(s):

P. Murugabharathi, B. Srutha Keerthi

Mathematics Division,
School of Advanced Sciences,
VIT Chennai, Vandaloor, Kelambakkam Road,
Chennai - 600 127, India.
E-mail: bharathi.muhi@gmail.com
E-mail: sruthilaya06@yahoo.co.in

Abstract:

In this work, considering a general subclass of bi-univalent Sakaguchi type functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in these classes. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

Paper's Title:

Classes of Meromorphic p-valent Parabolic Starlike Functions with Positive Coefficients

Author(s):

S. Sivaprasad Kumar, V. Ravichandran, and G. Murugusundaramoorthy

Department of Applied Mathematics
Delhi College of Engineering,
Delhi 110042, India
sivpk71@yahoo.com

School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics
Vellore Institute of Technology (Deemed University)
Vellore 632 014, India
gmsmoorthy@yahoo.com

Abstract:

In the present paper, we consider two general subclasses of meromorphic p-valent starlike functions with positive coefficients and obtain a necessary and sufficient condition for functions to be in these classes. Also we obtain certain other related results as a consequences of our main results.

Paper's Title:

On the Hohov Convolution Of The Class S_p(α,β)

Author(s):

T. N. Shanmugam and S. Sivasubramanian

Department of Mathematics,
Anna University,
Chennai 600025,
Tamilnadu, India.
shan@annauniv.edu

Department of Mathematics,
Easwari Engineering College,
Chennai-600089,
Tamilnadu, India,
sivasaisastha@rediffmail.com

Abstract:

Let F(a,b;c;z) be the Gaussian hypergeometric function and I_a,b;c(f)=zF(a,b;c;z)*f(z) be the Hohlov operator defined on the class A of all normalized analytic functions. We determine conditions on the parameters a,b,c such that I_a,b;c(f) will be in the class of parabolic starlike functions S_p(α,β). Our results extend several earlier results.

Paper's Title:

Approximation of Derivatives in a Singularly Perturbed Second Order Ordinary Differential Equation with Discontinuous Terms Arising in Chemical Reactor Theory

Author(s):

R. Mythili Priyadharshini and N. Ramanujam

Department of Mathematics, Bharathidasan University,
Tiruchirappalli - 620 024, Tamilnadu, India.
matram2k3@yahoo.com
URL: http://www.bdu.ac.in/depa/science/ramanujam.htm

Abstract:

In this paper, a singularly perturbed second order ordinary differential equation with a discontinuous convection coefficient arising in chemical reactor theory is considered. A robust-layer-resolving numerical method is suggested. An ε-uniform global error estimate for the numerical solution and also to the numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

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