References
- Zill DG. Differential equations with boundary-value problems. Nelson Education; 2016 Dec 5.
- Nievergelt Y, Nievergelt Y. Wavelets made easy. Boston: Birkhäuser; 1999 Apr.
- Koç A, Bartan B, Gundogdu E, Çukur T, Ozaktas HM. Sparse representation of two-and three-dimensional images with fractional Fourier, Hartley, linear canonical, and Haar wavelet transforms. Expert Systems with Applications. 2017 Jul 1; 77 : 247-55.
- Naresh Berwal, Dinesh Panchal and C.L. Parihar “Solution of Differential Equations Based on HAAR Operational Matrix”, Palestine Journal of Mathematics Vol. 3(2) (2014) , 281–288
- Mohammad Heydari, Zakieh Avazzadeh, Narges Hosseinzadeh,” Haar Wavelet Method for Solving High-Order Differential Equations with Multi-Point Boundary Conditions”, J. Appl. Comput. Mech., 7(2) (2021) xx-xx DOI: 10.22055/JACM.2020.31860.1935.
- A. Padmanabha Reddy, Manjula S. H., C. Sateesha and N. M. Bujurke Haar Wavelet Approach for the Solution of Seventh Order Ordinary Differential Equations, Vol. 3, No. 2, June 2016, pp. 108-114, Mathematical Modelling of Engineering Problems.
- A. Padmanabha Reddy, C. Sateesha and Manjula S.H. “Investigation of Haar Wavelet Collocation Method to Solve Ninth Order Boundary Value Problems”, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 5 (2017), pp. 1415-1428.
- [8] Lepik Ü “Numerical solution of differential equations using Haar wavelets” Mathematics and Computers in Simulation 68 (2005) 127–143 doi: 10.1016/j.matcom.2004.10.005
- Lepik Ü. Haar wavelet method for solving higher order differential equations. Int. J. Math. Comput. 2008 Nov 30;1(8):84-94.
- Chang P, Piau P. Haar wavelet matrices designation in numerical solution of ordinary differential equations. IAENG International Journal of Applied Mathematics. 2008 Aug; 38(3): 1-5.
- Berwal N, Panchal D, Parihar CL. Solution of differential equations based on Haar operational matrix. Palestine Journal of Mathematics. 2014 Sep 1;3(2):281-8.
- Majak J, Pohlak M, Eerme M, Shvartsman B. Solving ordinary differential equations with higher order Haar wavelet method. In AIP Conference Proceedings 2019 Jul 24 (Vol. 2116, No. 1, pp. 330002). AIP Publishing LLC.
- Swaidan W, Hussin A. Haar Wavelet Method for Constrained Nonlinear Optimal Control Problems with Application to Production Inventory Model. Sains Malaysiana. 2016 Feb 1; 45(2) : 305-13.
- Chen CF, Hsiao CH. Haar wavelet method for solving lumped and distributed-parameter systems. IEE Proceedings-Control Theory and Applications. 1997 Jan 1; 144(1): 87-94. doi: 10.1049/ip-cta:19970702
- Hsiao CH, Wu SP. Numerical solution of time-varying functional differential equations via Haar wavelets. Applied Mathematics and Computation. 2007 May 1; 188(1): 1049-58. doi: 10.1016/j.amc.2006.10.070
- Hahn B, Valentine D. Essential MATLAB for engineers and scientists. Academic Press; 2016 Sep.
- Fatunla SO. Numerical methods for initial value problems in ordinary differential equations. Academic Press; 2014 May 10.