Log in

Relevant bibliographies by topics / Clenshaw method / Journal articles

To see the other types of publications on this topic, follow the link: Clenshaw method.

Journal articles on the topic 'Clenshaw method'

Author: Grafiati

Published: 3 June 2025

Last updated: 20 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 43 journal articles for your research on the topic 'Clenshaw method.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

VITANCOL, ROBERTO S., and ERIC A. GALAPON. "APPLICATION OF CLENSHAW–CURTIS METHOD IN CONFINED TIME OF ARRIVAL OPERATOR EIGENVALUE PROBLEM." International Journal of Modern Physics C 19, no. 05 (2008): 821–44. http://dx.doi.org/10.1142/s0129183108012534.

Full text

Abstract:

The Clenshaw–Curtis method in discretizing a Fredholm integral operator is applied to solving the confined time of arrival operator eigenvalue problem. The accuracy of the method is measured against the known analytic solutions for the noninteracting case, and its performance compared against the well-known Nystrom method. It is found that Clenshaw–Curtis's is superior to Nystrom's. In particular, Nystrom method yields at most five correct decimal places for the eigenvalues and eigenfunctions, while Clenshaw–Curtis yields eigenvalues correct to 16 decimal places and eigenfunctions up to 15 dec

APA, Harvard, Vancouver, ISO, and other styles

2

Al-Towaiq, Mohammad, Marwan Alquran, and Osama Al-Khazaleh. "A modified algorithm for the Clenshaw-Curtis method." Journal of Information and Optimization Sciences 38, no. 3-4 (2017): 455–69. http://dx.doi.org/10.1080/02522667.2016.1224460.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Saravi, Masoud. "On the Clenshaw Method for Solving Linear Ordinary Differential Equations." American Journal of Computational and Applied Mathematics 1, no. 2 (2012): 74–77. http://dx.doi.org/10.5923/j.ajcam.20110102.14.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

SAIRA and Wen-Xiu Ma. "An Approximation Method to Compute Highly Oscillatory Singular Fredholm Integro-Differential Equations." Mathematics 10, no. 19 (2022): 3628. http://dx.doi.org/10.3390/math10193628.

Full text

Abstract:

This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a Taylor series expansion. A system of linear equations of FIDEs obtained by using equally spaced points as collocation points is solved to obtain the unknown function. The proposed method attains higher accuracy rates, which are proven by error analysis and some numerical examples as well.

APA, Harvard, Vancouver, ISO, and other styles

5

Katani, Roghayeh, and Fatemeh Pourahmad. "A collocation method for a class of Fredholm integral equations with highly oscillatory kernels." Asian-European Journal of Mathematics 11, no. 05 (2018): 1850076. http://dx.doi.org/10.1142/s1793557118500766.

Full text

Abstract:

In this paper, a collocation method by using Clenshaw–Curtis points is proposed to solve the Fredholm integral equations (FIEs) with highly oscillatory kernels. The collocation method is being applied to graded and uniform meshes. Due to the highly oscillatory kernels of integral equations, the discretized collocation equation will lead to the computation of the oscillatory integrals which will be computed by using the efficient Filon-type method. Finally, the effectiveness and accuracy of the proposed method are confirmed by numerical examples.

APA, Harvard, Vancouver, ISO, and other styles

6

Platov, Alexander J., and Juri I. Platov. "Efficient computation of ship’s wave-making resistance using michell’s integral." Russian Journal of Water Transport, no. 73 (December 20, 2022): 206–15. http://dx.doi.org/10.37890/jwt.vi73.327.

Full text

Abstract:

The aim of the present paper is to find efficient method of computation the wave-making resistance of a ship using mitchell’s integral. The computational schemes described in publications suggest the use of simple quadratures (trapezoidal and Simpson’s rule) with a fixed number of integration’s intervals. This approach assumes manual setup of the algorithm for calculating the wave-making resistance for each new ship and makes it difficult to estimate the error of the obtained results. It is shown that the use of these simple quadratures makes it possible to obtain reliable results, but at the

APA, Harvard, Vancouver, ISO, and other styles

7

Ma, Junjie. "Implementing the complex integral method with the transformed Clenshaw–Curtis quadrature." Applied Mathematics and Computation 250 (January 2015): 792–97. http://dx.doi.org/10.1016/j.amc.2014.09.098.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Honarvar Shakibaei Asli, Barmak, and Maryam Horri Rezaei. "Four-Term Recurrence for Fast Krawtchouk Moments Using Clenshaw Algorithm." Electronics 12, no. 8 (2023): 1834. http://dx.doi.org/10.3390/electronics12081834.

Full text

Abstract:

Krawtchouk polynomials (KPs) are discrete orthogonal polynomials associated with the Gauss hypergeometric functions. These polynomials and their generated moments in 1D or 2D formats play an important role in information and coding theories, signal and image processing tools, image watermarking, and pattern recognition. In this paper, we introduce a new four-term recurrence relation to compute KPs compared to their ordinary recursions (three-term) and analyse the proposed algorithm speed. Moreover, we use Clenshaw’s technique to accelerate the computation procedure of the Krawtchouk moments (K

APA, Harvard, Vancouver, ISO, and other styles

9

SAIRA and Shuhuang Xiang. "Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels." Symmetry 11, no. 6 (2019): 728. http://dx.doi.org/10.3390/sym11060728.

Full text

Abstract:

In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, ⨍ − 1 1 f ( x ) log ( x − α ) e i k x x − t d x , t ∉ ( − 1 , 1 ) , α ∈ [ − 1 , 1 ] for a smooth function f ( x ) . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some exam

APA, Harvard, Vancouver, ISO, and other styles

10

Kim, Changho, Sang Dong Kim, and Jungho Yoon. "Generalized Clenshaw–Curtis quadrature rule with application to a collocation least-squares method." Applied Mathematics and Computation 190, no. 1 (2007): 781–89. http://dx.doi.org/10.1016/j.amc.2007.01.095.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Lin, Fu-Rong, Xi Yang, and Gui-Rong Zhang. "Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients." Applied Numerical Mathematics 217 (November 2025): 112–25. https://doi.org/10.1016/j.apnum.2025.06.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Luo, Yao, and Xinyi Yang. "Impedance Variation in a Coaxial Coil Encircling a Metal Tube Adapter." Sensors 23, no. 19 (2023): 8302. http://dx.doi.org/10.3390/s23198302.

Full text

Abstract:

The impedance change in an induction coil surrounding a metal tube adapter is investigated using the truncated region eigenfunction expansion (TREE) method. The conventional TREE method is inapplicable to this problem as a consequence of the numerical overflow of the eigenfunctions of the air–metal multi-subdomain regions. The difficulty is surmounted by a normalization procedure for the numerical eigenfunctions obtained from the 1D finite element method (FEM). An efficient algorithm is devised by the Clenshaw–Curtis quadrature rule for integrals involving the numerical eigenfunctions. The num

APA, Harvard, Vancouver, ISO, and other styles

13

Niu, Cuixia, Huiqing Liao, Heping Ma, and Hua Wu. "Approximation Properties of Chebyshev Polynomials in the Legendre Norm." Mathematics 9, no. 24 (2021): 3271. http://dx.doi.org/10.3390/math9243271.

Full text

Abstract:

In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev–Gauss–Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre–Chebyshev spectral method. These results are also useful in Clenshaw–Curtis quadrature which is based on sampli

APA, Harvard, Vancouver, ISO, and other styles

14

Sweilam, Nasser Hassan, Tamer Mostafa Al-Ajami, and Ronald H. W. Hoppe. "Numerical Solution of Some Types of Fractional Optimal Control Problems." Scientific World Journal 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/306237.

Full text

Abstract:

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz met

APA, Harvard, Vancouver, ISO, and other styles

15

Hadi Noori Skandari, Mohammad, Marzieh Habibli, and Alireza Nazemi. "A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems." Mathematical Control & Related Fields 10, no. 1 (2020): 171–87. http://dx.doi.org/10.3934/mcrf.2019035.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Jwamer, K. H. F., Sh Sh Ahmed, and D. Kh Abdullah. "Approximate Solution of Volterra Integro-Fractional Differential Equations Using Quadratic Spline Function." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (2021): 50–64. http://dx.doi.org/10.31489/2021m1/50-64.

Full text

Abstract:

In this paper, we suggest two new methods for approximating the solution to the Volterra integro-fractional differential equation (VIFDEs), based on the normal quadratic spline function and the second method used the Richardson Extrapolation technique the usage of discrete collocation points. The fractional derivatives are regarded in the Caputo perception. A new theorem for the Richardson Extrapolation points for using the finite difference approximation of Caputo derivative is introduced with their proof. New techniques using the first derivative at the initial point such that obtained by fo

APA, Harvard, Vancouver, ISO, and other styles

17

Pimenov, V. G., and A. S. Hendy. "Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/510875.

Full text

Abstract:

Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shi

APA, Harvard, Vancouver, ISO, and other styles

18

Kang, Hongchao, and Xinping Shao. "Fast Computation of Singular Oscillatory Fourier Transforms." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/984834.

Full text

Abstract:

We consider the problem of the numerical evaluation of singular oscillatory Fourier transforms ∫ab‍x-aαb-xβf(x)eiωxdx, whereα>-1 and β>-1. Based on substituting the original interval of integration by the paths of steepest descent, iffis analytic in the complex regionGcontaining [a,b], the computation of integrals can be transformed into the problems of integrating two integrals on [0, ∞) with the integrand that does not oscillate and decays exponentially fast, which can be efficiently computed by using the generalized Gauss Laguerre quadrature rule. The efficiency and the validity of th

APA, Harvard, Vancouver, ISO, and other styles

19

Háková, Lenka, Jiří Hrivnák, and Lenka Motlochová. "ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS." Acta Polytechnica 56, no. 3 (2016): 202. http://dx.doi.org/10.14311/ap.2016.56.0202.

Full text

Abstract:

The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems. The diagram containing the relations among the special functions associated to the Weyl group orbit functions is presented and the link between the Weyl group orbit functions and the Jacobi polynomials is explicitly derived in full generality. The four cubature rules corresponding to these polynomials are summarized for all simple Lie algebras and their properties simultaneously tested on model functions. The

APA, Harvard, Vancouver, ISO, and other styles

20

Patra, Pritikanta, Debasish Das, and Rajani Ballav Dash. "Numerical Approximation of Surface Integrals Using Mixed Cubature Adaptive Scheme." Annals of Pure and Applied Mathematics 22, no. 01 (2020): 29–39. http://dx.doi.org/10.22457/apam.v22n1a05678.

Full text

Abstract:

This research described the development of a new mixed cubature rule for evaluation of surface integrals over rectangular domains. Taking the linear combination of Clenshaw-Curtis 5- point rule and Gauss-Legendre 3-point rule ( each rule is of same precision i.e. precision 5) in two dimensions the mixed cubature rule of higher precision was formed (i.e. precision 7). This method is iterative in nature and relies on the function values at uneven spaced points on the rectangle of integration. Also as supplement, an adaptive cubature algorithm is designed in order to reinforce our mixed cubature

APA, Harvard, Vancouver, ISO, and other styles

21

Mallick, Subhashis, and L. Neil Frazer. "Practical aspects of reflectivity modeling." GEOPHYSICS 52, no. 10 (1987): 1355–64. http://dx.doi.org/10.1190/1.1442248.

Full text

Abstract:

This paper is intended to help those not familiar with the “lore” of layered earth modeling to avoid some common problems. In the computation of the reflectivity function, an easily incorporated phase‐integral approximation is used away from turning points when the velocity gradient is smaller than the frequency. Hanning windows, or segments thereof, work well for both the slowness integral and the frequency integral. For the quadrature of the slowness integral the Filon method of Frazer is easily coded and vectorizes well; Levin’s Filon method and the Clenshaw‐Curtis‐Filon method of Xu and Ma

APA, Harvard, Vancouver, ISO, and other styles

22

Xu, Qimen, Xin Jing, Boqin Zhang, John E. Pask, and Phanish Suryanarayana. "Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature." Journal of Chemical Physics 156, no. 9 (2022): 094105. http://dx.doi.org/10.1063/5.0082523.

Full text

Abstract:

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. We present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms o

APA, Harvard, Vancouver, ISO, and other styles

23

Ma, Junjie. "Fast and high-precision calculation of earth return mutual impedance between conductors over a multilayered soil." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 3 (2018): 1214–27. http://dx.doi.org/10.1108/compel-09-2017-0408.

Full text

Abstract:

Purpose Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications. Design/methodology/approach According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differenti

APA, Harvard, Vancouver, ISO, and other styles

24

COONJOBEHARRY, RADHA KRISHN, DÉSIRÉ YANNICK TANGMAN, and MUDDUN BHURUTH. "A TWO-FACTOR JUMP-DIFFUSION MODEL FOR PRICING CONVERTIBLE BONDS WITH DEFAULT RISK." International Journal of Theoretical and Applied Finance 19, no. 06 (2016): 1650046. http://dx.doi.org/10.1142/s0219024916500461.

Full text

Abstract:

The current literature on convertible bonds (CBs) comprises only models where the stock price and the interest rate are governed by pure-diffusion processes. This paper fills a gap by developing and implementing a two-factor model where both underlying factors follow jump-diffusion processes, and which also incorporates default risk. We derive the partial integro-differential equation satisfied by the CB price in our model, and solve it by a spectral method based on Chebyshev discretizations and Clenshaw–Curtis quadratures. The conversion, call, and put constraints give rise to a linear comple

APA, Harvard, Vancouver, ISO, and other styles

25

Liu, Yang, Yulai Zhao, Jintao Li, Fangquan Xi, Shuanghe Yu, and Ye Zhang. "Research on Fault Feature Extraction Method Based on NOFRFs and Its Application in Rotor Faults." Shock and Vibration 2019 (July 2, 2019): 1–11. http://dx.doi.org/10.1155/2019/3524948.

Full text

Abstract:

Rub-impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain-based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high-orde

APA, Harvard, Vancouver, ISO, and other styles

26

Xiang, S., Y. Je Cho, H. Wang, and H. Brunner. "Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications." IMA Journal of Numerical Analysis 31, no. 4 (2011): 1281–314. http://dx.doi.org/10.1093/imanum/drq035.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Barrio, Roberto, and Jean-Claude Berges. "Perturbation Simulations of Rounding Errors in the Evaluation of Chebyshev Series." JUCS - Journal of Universal Computer Science 4, no. (6) (1998): 561–73. https://doi.org/10.3217/jucs-004-06-0561.

Full text

Abstract:

This paper presents some numerical simulations of rounding errors produced during evaluation of Chebyshev series. The simulations are based on perturbation theory and use recent software called AQUARELS. They give more precise results than the theoretical bounds (the difference is of some orders of magnitude). The paper concludes by confirming theoretical results on the increment of the error at the end of the interval [-1; 1] and the increased performance achieved by some modifications to Clenshaw's algorithm near those points.

APA, Harvard, Vancouver, ISO, and other styles

28

Janchuk, Petro. "DATA PROCESSING IN PYTHON: FOURIER-JACOBI SUMS AND THEIR DERIVATIVES." Grail of Science, no. 40 (June 25, 2024): 338–46. http://dx.doi.org/10.36074/grail-of-science.07.06.2024.051.

Full text

Abstract:

The use of software tools like SciPy abstracts the complexity of computational implementations. By importing specific functions from this library, users can efficiently perform operations such as polynomial evaluation, differentiation, and series expansion without delving into the intricate algorithmic details. The abstraction continues with the application of Clenshaw’s algorithm, a strategy used across different polynomial types to optimize the computation of series coefficients and derivatives efficiently. This algorithm serves as a universal tool in the computational toolkit, abstracting a

APA, Harvard, Vancouver, ISO, and other styles

29

Janchuk, Petro. "DATA PROCESSING IN PYTHON: FOURIER-JACOBI SUMS AND THEIR DERIVATIVES." Grail of Science, no. 39 (May 21, 2024): 314–21. http://dx.doi.org/10.36074/grail-of-science.10.05.2024.047.

Full text

Abstract:

The use of software tools like SciPy abstracts the complexity of computational implementations. By importing specific functions from this library, users can efficiently perform operations such as polynomial evaluation, differentiation, and series expansion without delving into the intricate algorithmic details. The abstraction continues with the application of Clenshaw’s algorithm, a strategy used across different polynomial types to optimize the computation of series coefficients and derivatives efficiently. This algorithm serves as a universal tool in the computational toolkit, abstracting a

APA, Harvard, Vancouver, ISO, and other styles

30

Rathi, Amit Kumar, and Arunasis Chakraborty. "Improved Moving Least Square-Based Multiple Dimension Decomposition (MDD) Technique for Structural Reliability Analysis." International Journal of Computational Methods 18, no. 01 (2020): 2050024. http://dx.doi.org/10.1142/s0219876220500243.

Full text

Abstract:

This paper presents the state-of-the-art on different moving least square (MLS)-based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity applications. The aim is to improve the performance of MLS-based dimension decomposition in terms of accuracy, number of function evaluations and computational time for large-dimensional problems. With this in view, multiple finite difference high dimension model representation (HDMR) scheme is developed. This anchored decomposition is implemented starting from an initial reference point and progress

APA, Harvard, Vancouver, ISO, and other styles

31

Xiang, S., Y. J. Cho, H. Wang, and H. Brunner. "Erratum to "Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications" (IMA Journal of Numerical Analysis (2011)31: 1281-1314)." IMA Journal of Numerical Analysis 33, no. 4 (2013): 1480–83. http://dx.doi.org/10.1093/imanum/drs052.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Kump, Patrizia, Cesare Hassan, Cristiano Spada, et al. "Efficacy and safety of a new low-volume PEG with citrate and simethicone bowel preparation for colonoscopy (Clensia): a multicenter randomized observer-blind clinical trial vs. a low-volume PEG with ascorbic acid (PEG-ASC)." Endoscopy International Open 06, no. 08 (2018): E907—E913. http://dx.doi.org/10.1055/a-0624-2266.

Full text

Abstract:

Abstract Background and study aims Quality of inspection during colonoscopy is strictly related to the level of cleansing. High-volume (PEG-based) solutions are highly effective and safe, but their high volume affects tolerability and compliance. The aim of this study was to compare a new low-volume PEG with citrate and simethicone solution (PMF 104,Clensia) with a low-volume PEG with ascorbic acid solution (PEG-ASC; Moviprep). Patients and methods This was a multicenter, randomized, observer-blind, parallel-group, phase 3 clinical trial, where patients were randomized between PMF 104 and PEG-

APA, Harvard, Vancouver, ISO, and other styles

33

M., Saravi, Ashrafi F., and Mirrajei S.R. "Numerical Solution of Linear Ordinary Differential Equations in Quantum Chemistry by Clenshaw Method." January 23, 2009. https://doi.org/10.5281/zenodo.1075994.

Full text

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or whe

APA, Harvard, Vancouver, ISO, and other styles

34

Sun, Mengjun, and Qinghua Wu. "On the Chebyshev spectral collocation method for the solution of highly oscillatory Volterra integral equations of the second kind." Applied Mathematics and Nonlinear Sciences 9, no. 1 (2024). http://dx.doi.org/10.2478/amns-2024-0757.

Full text

Abstract:

Abstract Based on Chebyshev spectral collocation and numerical techniques for handling highly oscillatory integrals, we propose a numerical method for a class of highly oscillatory Volterra integral equations frequently encountered in engineering applications. Specifically, we interpolate the unknown function at Chebyshev points, and substitute these points into the integral equation, resulting in a system of linear equations. The highly oscillatory integrals are treated using either the numerical steepest descent method or the Filon-Clenshaw-Curtis method. Additionally, we derive an error est

APA, Harvard, Vancouver, ISO, and other styles

35

Sweilam, N. H., A. M. Nagy, and T. M. Al-Ajami. "Numerical solutions of fractional optimal control with Caputo–Katugampola derivative." Advances in Difference Equations 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13662-021-03580-w.

Full text

Abstract:

AbstractIn this paper, we present a numerical technique for solving fractional optimal control problems with a fractional derivative called Caputo–Katugampola derivative. This derivative is a generalization of the Caputo fractional derivative. The proposed technique is based on a spectral method using shifted Chebyshev polynomials of the first kind. The Clenshaw and Curtis scheme for the numerical integration and the Rayleigh–Ritz method are used to estimate the state and control variables. Moreover, the error bound of the fractional derivative operator approximation of Caputo–Katugampola is d

APA, Harvard, Vancouver, ISO, and other styles

36

Klein, Christian, and Nikola Stoilov. "Multidomain spectral approach to rational‐order fractional derivatives." Studies in Applied Mathematics, January 18, 2024. http://dx.doi.org/10.1111/sapm.12671.

Full text

Abstract:

AbstractWe propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying curve ensuring analyticity of the respective integrands, the integrals over the different domains are computed with a Clenshaw–Curtis algorithm. As an example, we consider solitary waves for fractional Korteweg‐de Vries equations and compare these to results obtained with a di

APA, Harvard, Vancouver, ISO, and other styles

37

Gao, Jing, and Gaoqin Chang. "A bivariate Filon-Clenshaw-Curtis method of the highly oscillatory integrals on a square." Journal of Computational and Applied Mathematics, October 2023, 115599. http://dx.doi.org/10.1016/j.cam.2023.115599.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Harbrecht, Helmut, and Marc Schmidlin. "Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM." Stochastics and Partial Differential Equations: Analysis and Computations, October 13, 2021. http://dx.doi.org/10.1007/s40072-021-00214-w.

Full text

Abstract:

AbstractElliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to com

APA, Harvard, Vancouver, ISO, and other styles

39

Babaee, Hessam, Sumanta Acharya, and Xiaoliang Wan. "Optimization of Forcing Parameters of Film Cooling Effectiveness." Journal of Turbomachinery 136, no. 6 (2013). http://dx.doi.org/10.1115/1.4025732.

Full text

Abstract:

An optimization strategy is described that combines high-fidelity simulations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2–2, using a pseudospectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical simulations (DNS) using spectral element method were performed to sample the f

APA, Harvard, Vancouver, ISO, and other styles

40

Holel, Moataz Abbas, and Sameer Qasim Hasan. "Studying The Necessary Optimality Conditions and Approximates a Class of Sum Two Caputo–Katugampola Derivatives for FOCPs." Iraqi Journal of Science, February 28, 2023, 842–54. http://dx.doi.org/10.24996/ijs.2023.64.2.30.

Full text

Abstract:

In this paper, the necessary optimality conditions are studied and derived for a new class of the sum of two Caputo–Katugampola fractional derivatives of orders (α, ρ) and( β,ρ) with fixed the final boundary conditions. In the second study, the approximation of the left Caputo-Katugampola fractional derivative was obtained by using the shifted Chebyshev polynomials. We also use the Clenshaw and Curtis formula to approximate the integral from -1 to 1. Further, we find the critical points using the Rayleigh–Ritz method. The obtained approximation of the left fractional Caputo-Katugampola derivat

APA, Harvard, Vancouver, ISO, and other styles

41

Majidian, Hassan. "A comparative study of Filon-type rules for oscillatory integrals." Journal of Numerical Analysis and Approximation Theory, March 6, 2024. http://dx.doi.org/10.33993/jnaat531-1380.

Full text

Abstract:

Our aim is to answer the following question: "Among the Filon-type methods for computing oscillatory integrals, which one is the most efficient in practice?". We first discuss why we should seek the answer among the family of Filon-Clenshaw-Curtis rules. A theoretical analysis accompanied by a set of numerical experiments reveals that the plain Filon-Clenshaw-Curtis rules reach a given accuracy faster than the (adaptive) extended Filon-Clenshaw-Curtis rules. The comparison is based on the CPU run-time for certain wave numbers (medium and large).

APA, Harvard, Vancouver, ISO, and other styles

42

Mitchell, William, Abbie Natkin, Paige Robertson, Marika Sullivan, Xuechen Yu, and Chenxin Zhu. "Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals." BIT Numerical Mathematics 63, no. 3 (2023). http://dx.doi.org/10.1007/s10543-023-00984-w.

Full text

Abstract:

AbstractGauss–Legendre quadrature, Clenshaw–Curtis quadrature and the trapezoid rule are powerful tools for numerical integration of analytic functions. For nearly singular problems, however, these standard methods become unacceptably slow. We discuss and generalize some existing methods for improving on these schemes when the location of the nearby singularity is known. We conclude with an application to some nearly singular surface integrals that arise in three-dimensional viscous fluid flow.

APA, Harvard, Vancouver, ISO, and other styles

43

Russo, Giusy, Patrizia Alvisi, Claudio Romano, et al. "Efficacy and Safety of a new Low-Volume PEG with Citrate and Simethicone bowel preparation for pediatric elective colonoscopy: a phase 3 RCT." Endoscopy International Open, January 22, 2024. http://dx.doi.org/10.1055/a-2251-3372.

Full text

Abstract:

Background Currently available PEG-based preparations continue to represent a challenge in children. The aim of this study was to compare the efficacy and safety of a new low-volume PEG preparation with a conventional PEG-electrolyte solution (PEG-ES) in children and adolescents. Methods This was a multicenter, randomized, observer-blind, parallel-group, phase III clinical trial, where patients were randomized between PMF104 (Clensia) and a conventional PEG-ES (Klean-Prep), and stratified by age stratum (2-<6;6-<12;12-<18 years). The primary endpoint was to test the non-inferiority of

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!