Wavelet adaptive algorithm for discrete pseudo-differential operators

Document Type : Research Articles

Authors

1 Bozorgmehr University Of Qaenat

2 Arak University

Abstract

In this study, we examine biorthogonal wavelets that are tailored to a specific discrete pseudo-differential equation ‎‎‎of the form $T_{\sigma}u = f$, where $T_{\sigma}$ is an invertible discrete pseudo-differential operator defined on ‎‎‎the lattice $\mathbb{Z}^{n}$ for every $f\in\ell^{2}(\mathbb{Z}^{n})‎$‎. Our focus is on computing Galerkin approximations ‎‎‎of the solution to this problem using an adaptive algorithm.‎

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