In this paper, we bring three theorems that enable us to approximate the solution of Ferdholm integral equations of the second kind. Then we use the Coifman wavelets or Coiflets as scaling functions for projection that satisfied the conditions of theorems for approximation. Also we use this projection to convert the integral equation to a Galerkin system, which is the most important of the expa...

In this paper, we consider using Galerkin projection methods for solving multiple linear systems A (i) x (i) = b (i) , for 1 i s, where the coeecient matrices A (i) and the right-hand sides b (i) are diierent in general. In particular, we focus on the seed projection method which generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed ...

In this paper static and dynamic response of nanotweezers composed of two carbon nanotube (CNT) arms are investigated. Taking into account a continuum model and considering the electrostatic actuation as well as the presence of the van der Waals forces, the static nonlinear equations are solved by a step by step linearization and Galerkin projection method. Simulating the closing dynamics of a ...

In this paper we study the two-dimensional version of the RungeKutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Preliminary numerical results showing ...

Abstract. In this paper, we consider the discontinuous Galerkin (DG) methods to solve linear hyperbolic equations with singular initial data. With the help of weight functions, the superconvergence properties outside the pollution region will be investigated. We show that, by using piecewise polynomials of degree k and suitable initial discretizations, the DG solution is (2k+1)-th order accurat...

In this paper we study the two-dimensional version of the RungeKutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Preliminary numerical results showing ...

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your effective field theory) presents a pedagogical introduction to projection-based, reduced-order emulators for applications low-energy nuclear physics. term emulator refers here fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these are not yet well-known phys...