Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in Rn. A second order accurate scheme is combined with… (More)

In this paper we consider the problem of generating a well sampled discrete representation of the Pareto manifold or the Pareto front corresponding to the equilibrium points of a multi-objective… (More)

The improvement of discretization algorithms for the approximate 'solution of nonlinear functional equations is considered. Extensions to the method of difference corrections by Fox are discussed and… (More)

We consider constrained biobjective optimization problems. One of the extant issues in this area is that of uniform sampling of the Pareto front. We utilize equispacing constraints on the vector of… (More)

H e r e the f u n c t i o n s co, f, g t a k e v a l u e s i n ]Rd; f and g a r e a s s u m e d to be s u f f i c i e n t l y s m o o t h , and we a l s o a s s u m e t h a t p r o b l e m (1.1) h a… (More)

A study of two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically will be presented in a series of papers. In this Part 1, it is shown how a… (More)

In this initial chapter we consider some of the basic methods used in the fitting of data by real and complex linear combinations of exponentials. We have selected the two classes of methods that are… (More)

An adaptive finite difference method for first order nonlinear systems of ordinary differential equations subject to multipoint nonlinear boundary conditions is presented. The method is based on a… (More)