Accurate Numerical Method for Singularly Perturbed Differential-Difference Equations with Mixed Shifts
Diddi
Kumara Swamy
Department of Mathematics, Christu Jyoti Institute of Technology and
Science, Jangaon, 506167, India.
author
Kolloju
Phaneendra
Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, 500004,India.
author
Y.N.
Reddy
Department of Mathematics, National Institute of Technology, Warangal,
506004, India.
author
text
article
2018
eng
This paper is concerned with the numerical solution of the singularly perturbed differential-difference equations with small shifts called delay and advanced parameters. A fourth order finite difference method with a fitting factor is proposed for the solution of the singularly perturbed differential-difference equations with mixed shifts. The delay and advanced shifts are managed by Taylor series and an asymptotically equivalent singularly perturbed two-point boundary value problem is obtained. A fitting factor is introduced in the fourth order finite difference scheme for the problem which takes care of the small values of the perturbation parameter. This fitting factor is obtained from the asymptotic solution of singular perturbations. Thomas algorithm is used to solve the discrete system of the difference scheme. Convergence of the proposed method is analyzed. Maximum absolute errors in comparison with the several numerical experiments aretabulated to illustrate the proposed method.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
110
122
http://www.kjm-math.org/article_57949_faad09b64d50416a8548558290d7ffba.pdf
dx.doi.org/10.22034/kjm.2018.57949
On Certain Results Involving a Multiplier Transformation in a Parabolic Region
Richa
Brar
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib-140407, Punjab, India.
author
Sukhwinder
Billing
Department of Mathematics, Sri Guru Granth Sahib World University ,
Fatehgarh Sahib-140407, Punjab, India.
author
text
article
2018
eng
We, here, obtain certain results in subordination form involving a multiplier transformation in a parabolic region. In particular, using different dominants in our main result, we derive certain results on parabolic starlikeness, starlikeness, convexity, uniform convexity, strongly starlikeness, close-to-convexity and uniform close-to-convexity of p-valent analytic functions as well as univalent analytic functions.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
123
143
http://www.kjm-math.org/article_60177_7ab19b219bbfb0fdfc4ef62533b63751.pdf
dx.doi.org/10.22034/kjm.2018.59751
More on Convergence Theory of Proper Multisplittings
Chinmay
Giri
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
author
Debasisha
Mishra
Department of Mathematics, National Institute of Technology Raipur, Raipur
492010, Chhattisgarh, India.
author
text
article
2018
eng
In this paper, we first prove a few comparison results between twoproper weak regular splittings which are useful in getting theiterative solution of a large class of rectangular (square singular)linear system of equations $Ax = b$, in a faster way. We then deriveconvergence and comparison results for proper weak regularmultisplittings.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
144
154
http://www.kjm-math.org/article_60178_45b35ce601f0a41c767c604a5ff62498.pdf
dx.doi.org/10.22034/kjm.2018.60178
Uniqueness of Meromorphic Functions with Regard to Multiplicity
Harina
Waghamore
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru-560056, INDIA
author
Naveenkumar
Sannappala
Department of Mathematics, Jnanabharathi Campus, Bangalore University,
Bengaluru-560056, INDIA
author
text
article
2018
eng
In this paper, we investigate the uniqueness problem on meromorphic functions concerning differential polynomials sharing one value. A uniqueness result which related to multiplicity of meromorphic function is proved in this paper. By using the notion of multilplicity our results will generalise and improve the result due to Chao Meng [10].
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
155
166
http://www.kjm-math.org/article_60179_60795f61bcd501613831c381bf36238c.pdf
dx.doi.org/10.22034/kjm.2018.60179
Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations
Ioannis K
Argyros
Department of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.
author
Santhosh
George
Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.
author
text
article
2018
eng
The local convergence analysis of iterative methods is important since it indicates the degree of difficulty for choosing initial points. In the present study we introduce generalized three step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative, which actually appears in the methods in contrast to earlier works using hypotheses on higher derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions, which is not given in earlier studies. Numerical examples conclude this study.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
167
177
http://www.kjm-math.org/article_63368_012c2c785e1430a9ff18422feb561db6.pdf
dx.doi.org/10.22034/kjm.2018.63368
Generalized Ricci Solitons on Trans-Sasakian Manifolds
Mohd
Siddiqi
Department of Mathematics, Jazan University, Faculty of Science, Jazan,
Kingdom of Saudi Arabia.
author
text
article
2018
eng
The object of the present research is to shows that a trans-Sasakian manifold, which also satisfies the Ricci soliton and generalized Ricci soliton equation, satisfying some conditions, is necessarily the Einstein manifold.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
178
186
http://www.kjm-math.org/article_63446_eabee94b9a3fd4c91d2e2429b5763ac2.pdf
dx.doi.org/10.22034/kjm.2018.63446
On a New Subclass of m-Fold Symmetric Biunivalent Functions Equipped with Subordinate Conditions
Emeka
Mazi
Department of Mathematics, Faculty of Science, University of Ilorin, Nigeria
author
Şahsene
Altinkaya
Department of Mathematics, Faculty of Science, Uludag University, 16059,
Bursa, Turkey.
author
text
article
2018
eng
In this paper, we introduce a new subclass of biunivalent function class $\Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric analytic functions. For functions of the subclass introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$ and also study the Fekete-Szegö functional estimate for this class. Consequences of the results are also discussed.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
187
197
http://www.kjm-math.org/article_63470_def95421626bd10dbaaaf7b380ff11dd.pdf
dx.doi.org/10.22034/kjm.2018.63470
Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition
Taki Eddine
Oussaeif
Department of Mathematics and Informatics., The Larbi Ben M'hidi
University, Oum El Bouaghi, Algeria.
author
Abdelfatah
Bouziani
Département de Mathématiques et Informatique, Université Larbi Ben M'hidi, Oum El Bouagui, B.P. 565, 04000, Algerie.
author
text
article
2018
eng
This paper is concerned with the existence and uniqueness of a strong solution for linear problem by using a functional analysis method, which is based on an energy inequality and the density of the range of the operator generated by the problem. Applying an iterative process based on results obtained from the linear problem, we prove the existence anduniqueness of the weak generalized solution of nonlinear hyperbolic Goursat problem with integral condition.
Khayyam Journal of Mathematics
Tusi Mathematical Research Group (TMRG) and Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with
The Center of Excellence in Analysis on Algebraic Structures)
2423-4788
4
v.
2
no.
2018
198
213
http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf
dx.doi.org/10.22034/kjm.2018.65161