Convergence theorem for the Haar wavelet based discretization method

On the accuracy of the Haar wavelet discretization method

“…The convergence theorem for HWDM considered has been proved by authors in [38]. It has been shown that the convergence rate of HWDM is two in the case of general n-th order ODE.…”

“…Current study can be regarded as extension/continuation of the paper [38]. It contains proof that in the case of fourth order ODE (covers wide class of solid mechanics problems, etc) the rate of convergence of HWDM can be improved from two to four by applying Richardson extrapolation method.…”

“…Recently, the research group of the current study has proved the convergence theorem for HWDM covering general n-th order ordinal differential equations ODE [38].…”

A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

“…Siraj-ul-Islam et al 8,9 proved the convergence of the Haar wavelet series. Majak et al 10,11 published a convergence theorem for solving ODEs using the wavelet method 1,2 . To the best of our knowledge, the convergence analysis of a wavelet-based method for solving PDEs has not been presented before.…”

Numerical Solution of Partial Integrodifferential Equations of Diffusion Type

“…Wavelets have been used for numerical solutions of integral equations [19], integrodifferential equations [20], fractional diffusion-wave equation [21], ordinary differential equations [22], and partial differential equations [23]. These methods employ various types of wavelets, which include Daubechies [24], Battle-Lemarie [25], and Haar wavelet [26][27][28].…”