Browsing by Author "Sermutlu, E."

Now showing 1 - 7 of 7

Citation - Scopus: 3
A close look at Newton–Cotes integration rules
(Cankaya University, 2019) Sermutlu, E.; Sermutlu, Emre; 17647; Matematik
Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one. © 2019, Cankaya University. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 4
A new quadrature routine for improper and oscillatory integrals
(Elsevier Science inc, 2007) Sermutlu, E.; Sermutlu, Emre; Eyyuboglu, H. T.; 17647; 7688; Matematik
In MATLAB environment, a new quadrature routine based on Gaussian quadrature rule has been developed. Its performance is evaluated for improper integrals, rapidly oscillating functions and other types of functions requiring a. large number of evaluations. This performance is compared against the other quadrature routines written for MATLAB in terms of capability, accuracy and computation time. It is found that our routine rates quite favourably. (c) 2006 Elsevier Inc. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 7
Calculation of average intensity via semi-analytic method
(Springer, 2010) Eyyuboglu, H. T.; Sermutlu, Emre; Sermutlu, E.; 7688; 17647; Matematik
We present a semi-analytic approach to the solution of the quadruple Huygens-Fresnel integral which is used to calculate the average receiver intensity of a source beam after it has propagated in a turbulent atmosphere. Our approach is based on a self-designed MATLAB function that reduces a quadruple integral to a single one by sequential operations using a form that is readily available from tables. In this manner exact numerical evaluations are obtained, whilst lengthy hand derivations are avoided. Additionally, the computation time of the new approach is not much different from that of the complete analytic solution. Two application examples are cited, also establishing agreement with our previously published results.
Citation - WoS: 57
Citation - Scopus: 62
Intensity fluctuations in J-Bessel-Gaussian beams of all orders propagating in turbulent atmosphere
(Springer, 2008) Eyyuboglu, H. T.; Sermutlu, Emre; Sermutlu, E.; Baykal, Y.; Cai, Y.; Korotkova, O.; 7688; 17647; 7812; Matematik
The scintillation index of a J (n) -Bessel-Gaussian beam of any order propagating in turbulent atmosphere is derived and numerically evaluated at transverse cross-sections with the aid of a specially designed triple integral routine. The graphical outputs indicate that, just like the previously investigated J (0)-Bessel-Gaussian beam, higher-order members of the family also offer favorable scintillation characteristics at large source sizes. This advantage is maintained against rising beam orders. Viewed along the propagation axis, beams with lower orders and smaller widths exhibit smaller values of the scintillation index at shorter propagation distances and large values at longer propagation distances. Further, it is shown that the scintillation index of the J (n) -Bessel-Gaussian beams (n > 0) is larger than that of the fundamental Gaussian and the J (0)-Bessel-Gaussian beams only near the on-axis points, while remaining smaller towards the edges of the beam.
Citation - WoS: 29
Citation - Scopus: 32
On almost periodic solutions for an impulsive delay logarithmic population model
(Pergamon-elsevier Science Ltd, 2010) Alzabut, Jehad; Alzabut, J. O.; Stamov, G. Tr.; Sermutlu, Emre; Sermutlu, E.; 17647; Matematik
By employing the contraction mapping principle and applying the Gronwall-Bellman inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solutions for an impulsive delay logarithmic population model. An example with its numerical simulations has been provided to demonstrate the feasibility of our results. (C) 2009 Elsevier Ltd. All rights reserved.
Citation - WoS: 33
Citation - Scopus: 34
Positive almost periodic solutions for a delay logarithmic population model
(Pergamon-elsevier Science Ltd, 2011) Alzabut, Jehad; Alzabut, J. O.; Stamov, G. T.; Sermutlu, Emre; Sermutlu, E.; 17647; Matematik
By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result. (C) 2010 Elsevier Ltd. All rights reserved.
Citation - WoS: 36
Citation - Scopus: 37
Scintillation advantages of lowest order Bessel-Gaussian beams
(Springer Heidelberg, 2008) Eyyuboglu, H. T.; Sermutlu, Emre; Baykal, Y.; Sermutlu, E.; Cai, Y.; 7688; 7812; 17647; Matematik
For a weak turbulence propagation environment, the scintillation index of the lowest order Bessel-Gaussian beams is formulated. Its triple and single integral versions are presented. Numerical evaluations show that at large source sizes and large width parameters, when compared at the same source size, Bessel-Gaussian beams tend to exhibit lower scintillations than the Gaussian beam scintillations. This advantage is lost however for excessively large width parameters and beyond certain propagation lengths. Large width parameters also cause rises and falls in the scintillation index of off-axis positions toward the edges of the received beam. Comparisons against the fundamental Gaussian beam are made on equal source size and equal power basis.