Keywords and phrases: Chebyshev’s wavelet of second kind, function approximation, numerical differentiation, numerical examples.
Received: October 9, 2022; Revised: December 14, 2022; Accepted: December 28, 2022; Published: January 6, 2023
How to cite this article: Inderdeep Singh and Preeti, Chebyshev wavelets based technique for numerical differentiation, Advances in Differential Equations and Control Processes 30(1) (2023), 15-25. http://dx.doi.org/10.17654/0974324323002
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] C. Cattani, Haar wavelet splines, J. Interdisciplinary Math. 4 (2001), 35-47. [2] C. Cattani, Haar wavelets based technique in evolution problems, Proceedings of Estonian Academic Science, Physics, Mathematics 53 (2004), 45-65. [3] U. Lepik, Numerical solution of differential equations using Haar wavelets, Mathematics and Computers in Simulation 68 (2005), 127-143. [4] I. Singh, Wavelet based method for solving generalized Burgers type equations, International Journal of Computational Materials Science and Engineering 8(4) (2009), 1-24. [5] A. Ali, M. A. Iqba and S. T. Mohyud-Din, Hermite wavelets method for boundary value problems, International Journal of Modern Applied Physics 3(1) (2013), 38-47. [6] N. A. Pirim and F. Ayaz, Hermite collocation method for fractional order differential equations, An International Journal of Optimization and Control: Theories and Applications 8(2) (2018), 228-236. [7] I. Singh and S. Kumar, Haar wavelet collocation method for solving nonlinear Kuramoto-Sivashinsky equation, Italian Journal of Pure and Applied Mathematics 39 (2018), 373-384. [8] I. Singh and S. Kumar, Haar wavelet method for some nonlinear Volterra integral equations of the first kind, Journal of Computational and Applied Mathematics 292 (2016), 541-552. [9] I. Singh and M. Kaur, Comparative study of wavelet methods for solving Bernoulli’s equation, Jnanabha 50(2) (2020), 106-113. [10] Z. Avazzadeh and M. Heydari, Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind, Computational and Applied Mathematics 31(1) (2012), 127-142. [11] L. Zhu and Q. Fan, Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet, Communications in Nonlinear Science and Numerical Simulation 17(6) (2012), 2333-2341. [12] E. Babolian and F. Fattahzadeh, Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration, Applied Mathematics and Computation 188(1) (2007), 417-426. [13] Y. Wang and Q. Fan, The second kind Chebyshev wavelet method for solving fractional differential equations, Applied Mathematics and Computation 218(17) (2012), 8592-8601. [14] F. Zhou and X. Xu, Numerical solution of the convection diffusion equations by the second kind Chebyshev wavelets, Applied Mathematics and Computation 247 (2014), 353-367. [15] A. Ali, M. A. Iqbal and S. T. Mohyud-Din, Chebyshev wavelets method for delay differential equations, Int. J. Mod. Math. Sci. 8(2) (2013), 102-110. [16] E. H. Doha, W. M. Abd-Elhameed and Y. H. Youssri, Second kind Chebyshev operational matrix algorithm for solving differential equations of Lane-Emden type, New Astronomy 23 (2013), 113-117. [17] M. H. Heydari, M. R. Hooshmandasl and F. M. Ghaini, A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type, Applied Mathematical Modelling 38(5-6) (2014), 1597-1606.
|