A new approach to numerical integration based on Coifman wavelets

• Autorzy: Dehda Bachir

Identyfikatory

DOI

10.17512/jamcm.2019.3.03

• Języki publikacji: EN

Abstrakty

EN

In this paper, we present a new approach based on Coifman wavelets to find approximate values of definite integrals. This approach overcomes both CAS and Haar wavelets and hybrid functions in terms of absolute errors. The algorithm based on Coifman wavelets can be easily extended to find numerical approximations for double and triple integrals. Illustrative examples implemented using Matlab show the efficiency and effectiveness of this new method.

Słowa kluczowe

EN

numerical integration; CAS wavelets; Haar wavelets; hybrid functions; Coiflets

PL

integracja numeryczna; falka Haara; falka CAS; falka Coiflet; funkcja hybrydowa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 3
• Strony: 31--44
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Dehda Bachir

• Department of Mathematics, Faculty of Exact Sciences, University of Echahid Hamma Lakhdar El-Oued, Algeria

Bibliografia

• [1] Francois, D. (2016). Revisited optimal error bounds for interpolatory integration rules. Advances in Numerical Analysis, Vol. 2016, 1-8, DOI: 10.1155/2016/3170595.
• [2] Sharifi, M.A., & Seif, M.R. (2014). A new family of multistep numerical integration methods based on Hermite interpolation. Celestial Mechanics and Dynamical Astronomy, 118(1), 29-48, DOI: 10.1007/s10569-013-9517-4.
• [3] Zlatko, U. (2006). Some modifications of the trapezoidal rule. Sarajevo Journal of Mathematics, 2(2), 237-245, http://www.anubih.ba/Journals/vol-2,no-2,y06/13revudovicic.pdf
• [4] Dehda, B., & Melkemi, K. (2017). Image denoising using new wavelet thresholding function. Journal of Applied Mathematics and Computational Mechanics, 16(2), 55-65, DOI: 10.17512/jamcm.2017.2.05.
• [5] Dehda, B., & Melkemi, K. (2016). Novel method for reduction of wavelet coefficients number and its applications in images compression. International Journal of Applied Mathematics and Machine Learning, 5(1), 43-65, DOI: 10.18642/ijamml_7100121693.
• [6] Imran, A. (2013). New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets. Journal of Computational and Applied Mathematics, 239, 333-345, DOI: 10.1016/j.cam.2012.08.031.
• [7] Rezabeyk, S., & Maleknejad, K. (2015). Application of CAS wavelet to construct quadrature rules for numerical integration. Int. J. Industrial Mathematics, 7(1), 87-92, http://ijim.srbiau.ac.ir/
• [8] Imran, A., & Fazal, H. (2010). A comparative study of numerical integration based on Haar wavelets and hybrid functions. Computers and Mathematics with Applications, 59(6), 2026-2036, DOI: 10.1016/j.camwa.2009.12.005.
• [9] Imran, A., & Wajid, K. (2011). Quadrature rules for numerical integration based on Haar wavelets and hybrid functions. Computers and Mathematics with Applications, 61, 2770-2781, DOI: 10.1016/j.camwa.2011.03.043.
• [10] Barzkar, A., & Assari, P. (2012). Application of the CAS Wavelet in solving Fredholm--Hammerstein integral equations of the second kind with error analysis. World Applied Sciences Journal, 18(12), 1695-1704, DOI: 10.5829/idosi.wasj.2012.18.12.467.
• [11] Černa, D., Finěk, V., & Najzar, K. (2008). On the exact values of coefficients of coiflets. Cent.Eur. J. Math., 6(1), 159-169, DOI: 10.2478/s11533-008-0011-2.
• [12] Xiaomin, W. (2014). A Coiflets-based wavelet Laplace method for solving the Riccati differential equations. Journal of Applied Mathematics, Vol. 2014, 1-8, DOI: 10.1155/2014/257049.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).