Fourier finite-difference (FFD) migration combines the complementary advantages of the phase-shift and finite-difference migration methods. However, as with other implicit finite-difference algorithms, direct application to 3-D problems is prohibitively expensive. Rather than making the simple x y splitting approximation that leads to extensive azimuthal operator anisotropy, I demonstrate an al...

ACKNOWLEDGEMENTS I would like to truly thank all of my committee members for their encouragement and guidance in the preparation of this thesis. I especially want to express my gratitude to Dr. Kevin Clarno for his insight and assistance. My advisor, Dr. Cassiano de Oliveira, has been immensely helpful with his continuous encouragement and unique perspectives. Perhaps most of all, I want to tha...

1. Introduction. In companion papers [l; 6] recently Peaceman, Rachford, and the author introduced a finite difference technique called therein the alternating direction implicit method for approximating the solution of transient and permanent heat flow problems in two space variables. The validity of the method was established only in the case of a rectangular domain. Since then the procedure ...

The Galerkin method is applied to a pair of functions. It is demonstrated that this system can be linear and then nonlinear primitive (wave) equations. efficiently solved by an implicit method. Numerical This results in a system of ordinary differential equations. examples show that integration using the Galerkin method Procedures are included for generating the coefficient is more efficient th...

Osmosis filters are based on drift–diffusion processes. They offer nontrivial steady states with a number of interesting applications. In this paper we present a fully discrete theory for linear osmosis filtering that follows the structure of Weickert’s discrete framework for diffusion filters. It regards the positive initial image as a vector and expresses its evolution in terms of iterative m...

Using classical finite difference schemes often generates numerical drawbacks such as spurious oscillations in the solution of the famous Black–Scholes partial differential equation. We analyze the fully implicit scheme, frequently used numerical method in Finance, that in the presence of discontinuous payoff and low volatility arises spurious oscillations. We propose a modification of this sch...

A thorough numerical assessment of Finite Difference Time Domain and Complex-Envelope Alternating-Direction-Implicit Finite-Difference-Time-Domain Methods has been carried out based on a basic single mode Plane Optical Waveguide structure. Simulation parameters for both methods were varied and the impact on the performance of both numerical methods is investigated.

We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.