Relevant bibliographies by topics / Clenshaw method

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Academic literature on the topic 'Clenshaw method'

Author: Grafiati
Published: 3 June 2025
Last updated: 20 July 2025

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Journal articles on the topic "Clenshaw method"

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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.

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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 decimal places for the same number of quadrature points. Moreover, Clenshaw–Curtis's accuracy in the eigenvalues is uniform over a determinable range of the computed eigenvalues for a given number of quadrature abscissas. Clenshaw–Curtis is then applied to the harmonic oscillator confined time of arrival operator eigenvalue problem.
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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.

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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.

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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.

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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.
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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.

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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.
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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.

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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 cost of tens of billions of calculations of the ship's surface function. The applicability of more advanced universal quadratures for calculating the mitchell’s integral is investigated: adaptive Newton-Cotes rules, Gauss-Kronrod rules and Clenshaw-Curtis quadratures. As a result, it is established that the Clenshaw-Curtis quadrature provides a reliable and efficient calculation of the mitchell’s integral. The computational scheme using this quadrature allows you to build an automatic algorithm for calculating the ship's wave-making resistance by type ship method.
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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.

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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.

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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 (KMs) using a fast digital filter structure to generate a lattice network for KPs calculation. The proposed method confirms the stability of KPs computation for higher orders and their signal reconstruction capabilities as well. The results show that the KMs calculation using the proposed combined method based on a four-term recursion and Clenshaw’s technique is reliable and fast compared to the existing recursions and fast KMs algorithms.
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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.

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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 examples.
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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.

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Book chapters on the topic "Clenshaw method"

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Mason, J. C., and E. Venturino. "Integration Methods of Clenshaw-Curtis Type, Based on Four Kinds of Chebyshev Polynomials." In Multivariate Approximation and Splines. Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8871-4_13.

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Conference papers on the topic "Clenshaw method"

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Babaee, Hessam, Sumanta Acharya, and Xiaoliang Wan. "Optimization of Forcing Parameters of Film Cooling Effectiveness." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95636.

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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 pseudo-spectral 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 film cooling effectiveness on a Clenshaw-Curtis grid in the design space. The geometry includes a 35-degree delivery tube and a plenum. It is observed that in the parameter space explored a global optimum exists, and in the present study, the best film cooling effectiveness is found at DC = 0.14 and St = 1.03. In the same range of DC and St, four other local optimums were found. The physical mechanisms leading to the forcing parameters of the global optimum are explored and ingestion of the crossflow into the delivery tube is observed to play an important role in this process. The gradient-based optimization algorithms are argued to be unsuitable for the current problem due to the non-convexity of the objective function.
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Swamy, Maharudrayya, Pejman Shoeibi Omrani, and Nestor Gonzalez Diez. "Uncertainty Quantification of Aeroacoustic Power Sources in Corrugated Pipes." In ASME 2015 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/pvp2015-45507.

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Gas transport in corrugated pipes often exhibit whistling behavior, due to periodic flow-induced pulsations generated in the pipe cavities. These aero-acoustic sources are strongly dependent on the geometrical dimensions and features of the cavities. As a result, uncertainties in the exact shape and geometry play a significant role in determining the singing behavior of corrugated pipes. While predictive modelling for idealized periodic structures is well established, this paper focusses on the sensitivity analysis and uncertainty quantification (UQ) of uncertain geometrical parameters using probabilistic models. The two most influential geometrical parameters varied within this study are the cavity width and downstream edge radius. Computational Fluid Dynamics (CFD) analysis was used to characterize the acoustic source. Stochastic collocation method was used for propagation of input parameter uncertainties. The analysis was performed with both full tensor product grid and sparse grid based on level-2 Clenshaw-Curtis points. The results show that uncertainties in the width and downstream edge radius of the cavity have an effect on the acoustic source power, peak Strouhal number and consequently the whistling onset velocity. Based on the assumed input parameters distribution functions, the confidence levels for the prediction of onset velocity were calculated. Finally, the results show the importance of performing uncertainty analysis to get more insights in the source of errors and consequently leading to a more robust design or risk-management oriented decision.
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Atallah, Ahmed, and Ahmad Bani Younes. "A Comparative Study of Orbit Propagation Using Gauss-Legendre and Clenshaw-Curtis Quadrature Methods." In AIAA SCITECH 2022 Forum. American Institute of Aeronautics and Astronautics, 2022. http://dx.doi.org/10.2514/6.2022-2511.

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Atallah, Ahmed, and Ahmad Bani Younes. "Correction: A Comparative Study of Orbit Propagation Using Clenshaw-Curtis and Gauss-Legendre Quadrature Methods." In AIAA SCITECH 2022 Forum. American Institute of Aeronautics and Astronautics, 2022. http://dx.doi.org/10.2514/6.2022-2511.c1.

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