NUMERICAL DIFFERENTIATION VIA HERMITE WAVELETS
Inderdeep Singh1, Manbir Kaur2
1,2 Department of Physical Sciences
Sant Baba Bhag Singh University
Jalandhar-144030, Punjab, INDIA

Abstract

In this research, numerical technique based on Hermite wavelets is established to find the numerical differentiation. Proposed technique is based on the expansion of unknown function into a series of basis of Hermite wavelets. Some numerical experiments have been performed to illustrate the accuracy of the proposed technique.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 5
Year: 2020

DOI: 10.12732/ijam.v33i5.6

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References

  1. [1] C. Cattani, Haar wavelet splines, J. Interdisciplinary Math., 4 (2001), 35-47.
  2. [2] C.F. Chen and C.H. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEEE Proc.: Part D, 144, No 1 (1997), 87-94.
  3. [3] C. Cattani, Haar wavelets based technique in evolution problems, Proc. of Estonian Academic Science, Physics, Mathematics, 53 (2004), 45-65.
  4. [4] C.F. Chen and C.H. Hsiao, Wavelet approach to Optimizing dynamic systems, IEE Proc. Control Theory and Applications, 146 (1997), 213-219.
  5. [5] U. Lepik, Numerical solution of differential equations using Haar wavelets, Mathematics and Computers in Simulation, 68 (2005), 127-143. NUMERICAL DIFFERENTIATION VIA HERMITE WAVELETS 831
  6. [6] U. Lepik, Application of Haar wavelet transform to solving integral and differential equations, Proc. of Estonian Academy of Science, Physics, Mathematics , 56, No 1 (2007), 28-46.
  7. [7] I. Singh, Wavelet based method for solving generalized Burgers type equations, International J. of Computational Materials Science and Engineering , 8, No 4 (2009), 1-24.
  8. [8] A. Ali, M.A. Iqba and S.T. Mohyud-din, Hermite wavelets method for boundary value problems, International J. of Modern Applied Physics, 3, No 1 (2013), 38-47.
  9. [9] N.A. Pirim, F. Ayaz, Hermite collocation method for fractional order differential equations, An International J. of Optimization and Control: Theories & Applications, 8, No 2 (2018), 228-236.
  10. [10] A.K. Gupta, S.S. Ray, An investigation with Hermite wavelets for accurate solution of fractional Jaulent-Miodek equation associated with energy dependent Schrodinger potential, Applied Mathematics and Computation, 270 (2015), 458-471.
  11. [11] O. Oruc, A numerical procedure based on Hermite wavelets for two dimensional hyperbolic telegraph equation, Engineering with Computers, 34, No 4 (2018), 741-755.
  12. [12] B.I. Khashem, Hermite wavelet approach to estimate solution for Bratu’s problem, Emirates J. for Engineering Research, 24, No 2 (2019), 1-4.
  13. [13] I. Singh, S. Kumar, Haar wavelet collocation method for solving nonlinear Kuramoto-Sivashinsky equation, Italian J. of Pure and Applied Mathematics , 39 (2018), 373-384.
  14. [14] S.C. Shiralashetti, K. Srinivasa, Hermite wavelets operational matrix of integration for the numerical solution of nonlinear singular initial value problems, Alexandria Engineering J., 57 (2018), 2591-2600.
  15. [15] I. Singh, S. Kumar, Haar wavelet method for some nonlinear Volterra integral equations of the first kind, J. of Computational and Applied Mathematics, 292 (2016), 541-552.