The paper is concerned with the wavelet-Galerkin method for the numerical solution of
Fredholm linear integral equations and second-order integro-differential equations. We …

The paper is concerned with the construction of a cubic spline wavelet basis on the unit
interval and an adaptation of this basis to the first-order homogeneous Dirichlet boundary …

This paper attempts to merge the concept of hierarchical finite element analysis (FEA) into
isogeometric analysis (IGA). The proposed methodology replaces the traditional grid …

This chapter is concerned with the study of the wavelet-Galerkin method for the numerical
solution of the second-order partial integro-differential equations on the product domains …

Due to its potential applications in image restoration and deep convolutional neural
networks, the study of irregular frames has interested some researchers. This paper …

This paper introduces a wavelet Galerkin method for solving two-dimensional elliptic
interface problems of the form in $-\nabla\cdot (a\nabla u)= f $ in $\Omega\backslash …

In this paper, we investigate 1D elliptic equations $-\nabla\cdot (a\nabla u)= f $ with rough
diffusion coefficients $ a $ that satisfy $0< a_ {\min}\le a\le a_ {\max}<\infty $ and $ f\in L_2 …

This paper is concerned with a construction of new quadratic spline wavelets on a bounded
interval satisfying homogeneous Dirichlet boundary conditions. The inner wavelets are …

The Sobolev space H ς (ℝ d), where ς> d/2, is an important function space that has many
applications in various areas of research. Attributed to the inertia of a measurement …

In this article, a pair of wavelets for Hermite cubic spline bases are presented. These
wavelets are in C 1 and supported on [− 1, 1]. These spline wavelets are then adapted to the …