scholarly journals Comparing the Performance of Four Sinc Methods for Numerical Indefinite Integration

2021 ◽  
pp. 7-41
Author(s):  
Richard Olatokunbo Akinola
Keyword(s):  
Numerical Approximation ◽  
Quadrature Formulas ◽  
Numerical Examples ◽  
Sinc Method ◽  
Cpu Time ◽  
The Third ◽  
Sinc Methods ◽  
Quadrature Methods ◽  
Double Exponential ◽  
Single Exponential

Aims/ Objectives: To compare the performance of four Sinc methods for the numerical approximation of indefinite integrals with algebraic or logarithmic end-point singularities. Methodology: The first two quadrature formulas were proposed by Haber based on the sinc method, the third is Stengers Single Exponential (SE) formula and Tanaka et al.s Double Exponential (DE) sinc method completes the number. Furthermore, an application of the four quadrature formulas on numerical examples, reveals convergence to the exact solution by Tanaka et al.s DE sinc method than by the other three formulae. In addition, we compared the CPU time of the four quadrature methods which was not done in an earlier work by the same author. Conclusion: Haber formula A is the fastest as revealed by the CPU time.

scholarly journals Closed expressions for coefficients in weighted Newton-Cotes quadratures

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Mohammad Masjed-Jamei ◽  
Gradimir Milovanovic ◽  
M.A. Jafari
Keyword(s):  
Short Note ◽  
Stirling Numbers ◽  
Quadrature Formulas ◽  
Numerical Examples ◽  
Quadrature Formulae ◽  
Equidistant Nodes

In this short note, we derive closed expressions for Cotes numbers in the weighted Newton-Cotes quadrature formulae with equidistant nodes in terms of moments and Stirling numbers of the first kind. Three types of equidistant nodes are considered. The corresponding program codes in Mathematica Package are presented. Finally, in order to illustrate the application of the obtained quadrature formulas a few numerical examples are included.

scholarly journals USULAN PERMINTAAN PRODUK SN 5 ML DI PT. XYZ DENGAN METODE TIME SERIES

2021 ◽  
Vol 8 (2) ◽  
pp. 117-122
Author(s):  
Sambas Sundana ◽  
Destri Zahra Al Gufronny
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Exponential Smoothing ◽  
Double Exponential ◽  
Double Exponential Smoothing ◽  
Single Exponential ◽  
Weighted Moving Average

Permasalahan yang dihadapi PT. XYZ yaitu kesulitan dalam menentukan jumlah permintaan produk yang harus tersedia untuk periode berikutnya agar tetap dapat memenuhi kebutuhan pelanggan dan tidak menyebabkan penumpukan barang dalam jangka waktu yang lama terutama produk SN 5 ML yang memiliki permintaan jumlah paling besar dari produk lainnya. Tujuan dari penelitian ini yaitu menentukan metode peramalan yang tepat untuk meramalkan jumlah permintaan produk SN 5 ml periode Januari sampai dengan Desember 2021 Metode yang digunakan dalam penelitian ini yaitu metode peramalan Moving Average (MA), Weighted Moving Average (WMA), Single Exponential Smoothing (SES), dan Double Exponential Smoothing (DES). Adapun langkah langkah peramalan yang dilakukan yaitu menentukan tujuan peramalan,memilih unsur apa yang akan diramal, menentukan horizon waktu peramalan (pendek, menengah, atau panjang), memilih tipe model peramalan, mengumpulkan data yang di perlukan untuk melakukan peramalan, memvalidasi dan menerapkan hasil peramalan Berdasarkan perhitungan didapat metode peramalan dengan persentase tingkat kesalahan terkecil dibandingkan dengan metode lainnya yaitu  metode Moving Average (MA) dengan hasil yang diperoleh permintaan produk SN 5 ML pada bulan Januari sampai dengan Desember 2021 yaitu sebanyak 22.844.583 unit

scholarly journals B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations

2004 ◽  
Vol 1 (2) ◽  
pp. 340-346
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equations ◽  
Spline Function ◽  
Cubic Spline ◽  
Second Order ◽  
Third Order ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
The Third ◽  
New Procedures

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

scholarly journals An Optimized Symmetric WENO Method-Based Numerical Simulation of Intense Sound Field Generated by Underwater Plasma Sound Source

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Kaizhuo Lei ◽  
Xiaolong Liu ◽  
Ning Li ◽  
Xuchao Fan
Keyword(s):  
Euler Equations ◽  
Sound Source ◽  
Sound Field ◽  
Maximum Error ◽  
Numerical Examples ◽  
Weighted Essentially Nonoscillatory ◽  
The Third ◽  
Calculation Results ◽  
Pulse Sound ◽  
Fifth Order

The intensive pulse sound wave can be generated by the underwater plasma sound source (UPSS) based on the discharge of the underwater high voltage. The distribution of the sound field is prominently nonlinear. In this paper, the sound field of the intensive UPSS is described by the integral two-dimensional axisymmetric unsteady Euler equations firstly. In order to solve the Euler equations numerically, an optimized fifth-order symmetric WENO (weighted essentially nonoscillatory) method based on the three templates is proposed which is called WENO-SYM3. Without increasing the number of candidate templates, a new symmetric template structure can be obtained by expanding the second template and shifting the third one backwards for one space. The method is validated through numerical examples and experiments, and the results show that WENO-SYM3 has a high distinguished accuracy; meanwhile, its nonphysical oscillations are not obvious. The experimental results are basically the same as the calculation results, and the maximum error is around 3%.

scholarly journals Numerical Approximation of the Space Fractional Cahn-Hilliard Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Zhifeng Weng ◽  
Langyang Huang ◽  
Rong Wu
Keyword(s):  
Numerical Approximation ◽  
Second Order ◽  
Differentiation Formula ◽  
Numerical Examples ◽  
Backward Differentiation Formula ◽  
Hilliard Equation ◽  
Order Case ◽  
Energy Stable ◽  
Cahn Hilliard Equation ◽  
Fourier Spectral Methods

In this paper, a second-order accurate (in time) energy stable Fourier spectral scheme for the fractional-in-space Cahn-Hilliard (CH) equation is considered. The time is discretized by the implicit backward differentiation formula (BDF), along with a linear stabilized term which represents a second-order Douglas-Dupont-type regularization. The semidiscrete schemes are shown to be energy stable and to be mass conservative. Then we further use Fourier-spectral methods to discretize the space. Some numerical examples are included to testify the effectiveness of our proposed method. In addition, it shows that the fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case.

Influence of exercise intensity on pulmonary oxygen uptake kinetics at the onset of exercise and recovery in male adolescents

2008 ◽  
Vol 33 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Nicola Lai ◽  
Melita M. Nasca ◽  
Marco A. Silva ◽  
Fatima T. Silva ◽  
Brian J. Whipp ◽  
...  
Keyword(s):  
Oxygen Uptake ◽  
Slow Component ◽  
Work Rate ◽  
Moderate Intensity ◽  
Heavy Exercise ◽  
Pulmonary Oxygen Uptake ◽  
Square Wave ◽  
Male Adolescents ◽  
Double Exponential ◽  
Single Exponential

The dynamics of the pulmonary oxygen uptake (VO2) responses to square-wave changes in work rate can provide insight into bioenergetic processes sustaining and limiting exercise performance. The dynamic responses at the onset of exercise and during recovery have been investigated systematically and are well characterized at all intensities in adults; however, they have not been investigated completely in adolescents. We investigated whether adolescents display a slow component in their VO2 on- and off-kinetic responses to heavy- and very heavy-intensity exercise, as demonstrated in adults. Healthy African American male adolescents (n = 9, 14–17 years old) performed square-wave transitions on a cycle ergometer (from and to a baseline work rate of 20 W) to work rates of moderate (M), heavy (H), and very heavy (VH) intensity. In all subjects, the VO2 on-kinetics were best described with a single exponential at moderate intensity (τ1, on = 36 ± 11 s) and a double exponential at heavy (τ1, on = 29 ± 9 s; τ2, on = 197 ± 92 s) and very heavy (τ1, on = 36 ± 9 s; τ2, on = 302 ± 14 s) intensities. In contrast, the VO2 off-kinetics were best described with a single exponential at moderate (τ1, off = 48 ± 9 s) and heavy (τ1, off = 53 ± 7 s) intensities and a double exponential at very heavy (τ1, off = 51 ± 3 s; τ2, off = 471 ± 54 s) intensity. In summary, adolescents consistently displayed a slow component during heavy exercise (on- but not off- transition) and very heavy exercise (on- and off-transitions). Although the overall response dynamics in adolescents were similar to those previously observed in adults, their specific characterizations were different, particularly the lack of symmetry between the on- and off-responses.

Fast 2-D ray+Born migration/inversion in complex media

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Philippe Thierry ◽  
Stéphane Operto ◽  
Gilles Lambaré
Keyword(s):  
Numerical Approximation ◽  
Reference Model ◽  
Real Data ◽  
Model Parameters ◽  
Complex Media ◽  
Inversion Algorithm ◽  
Numerical Approximations ◽  
Data Set ◽  
Cpu Time ◽  
Computational Evaluation

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

Preparation and Luminescence of Europium Doped Zinc Silicate Phosphor

1999 ◽  
Vol 560 ◽  
Author(s):  
H. X. Zhang ◽  
Y. Zhou ◽  
C. H. Kam ◽  
Y. L. Lam ◽  
Y. C. Chan
Keyword(s):  
Decay Time ◽  
Sol Gel ◽  
Xrd Analysis ◽  
Luminescence Decay ◽  
Zinc Silicate ◽  
Silicate Phosphor ◽  
Slow Decay ◽  
Double Exponential ◽  
Triclinic Structure ◽  
Single Exponential

ABSTRACTEuropium doped zinc silicate (Eu:Zn2SiO4) phosphors in the forms of nanoscale powder and film has been prepared by sol-gel method. XRD analysis indicz: ed that the powders have willemite structure with a small amount of triclinic structure and the filn has, pure willemite structure. Photoluminescence measurement showed that strong red emission of Eu3+5D0→7 F2transition could be obtained under excitation at both 256 and 393 nm. Luminescence decay of the emission under 393 nm excitation can be fitted by a single exponential, yielding a decay time τ =1.43 ms; and the luminescence under 256 nm excitation shows double exponential decay with a slow decay time τs,=2.13 ms and a fast decay time τf =2.05 ms.

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