Numerical solution of differential equations using Haar wavelets

Ü. Lepik

Mathematics and Computers in Simulation (MATCOM), 2005, vol. 68, issue 2, 127-143

Abstract: Haar wavelet techniques for the solution of ODE and PDE is discussed. Based on the Chen–Hsiao method [C.F. Chen, C.H. Hsiao, Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc.—Control Theory Appl. 144 (1997) 87–94; C.F. Chen, C.H. Hsiao, Wavelet approach to optimising dynamic systems, IEE Proc. Control Theory Appl. 146 (1997) 213–219] a new approach—the segmentation method—is developed. Five test problems are solved. The results are compared with the result obtained by the Chen–Hsiao method and with the method of piecewise constant approximation [C.H. Hsiao, W.J. Wang, Haar wavelet approach to nonlinear stiff systems, Math. Comput. Simulat. 57 (2001) 347–353; S. Goedecker, O. Ivanov, Solution of multiscale partial differential equations using wavelets, Comput. Phys. 12 (1998) 548–555].

Keywords: Haar wavelets; Differential equations; Segmentation method; Collocation method (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:68:y:2005:i:2:p:127-143

DOI: 10.1016/j.matcom.2004.10.005

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