Numerical solution of differential equations using Haar wavelets

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].