Abstract: The finite-difference method is an important approach for solving boundary-value problems of nonlinear ordinary and partial differential equations. In this approach, derivatives and partial ...

Finite difference methods have become a cornerstone in the simulation of seismic wave propagation, providing a robust numerical framework to approximate the differential equations that govern seismic ...

The generalized local maximum principle for a difference operator $L_h$ asserts that if $L_hu(x) > 0$ then $\Gamma u$ cannot attain its positive maximum at the net ...

In this paper, a short review of the calculus of exact finite-differences of integer order is proposed. The finite-difference operators are called the exact finite-differences of integer orders, if ...

Abstract: A systematic approach to the construction of hybrid time- and frequency-domain algorithms derived from finite-difference operators is presented. The idea originates from projection formalism ...

ABSTRACT: Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly ...

This repository contains the code for implementing the finite-difference forward, adjoint, and gradient operators for the groundwater flow equation. The operators are implemented via Devito, a ...

Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic ...