Difference equations and iterative processes

Divergence equations and iterative processe

Computation of Generalized Averaged Gaussian Quadrature Rules

The estimation of the quadrature error of a Gauss quadrature rule when applied to the approximation of an integral determined by a real-valued integrand and a real-valued nonnegative measure with support on the real axis is an important problem in scientific computing. Laurie [2] developed anti-Gauss quadrature rules as an aid to estimate this error. Under suitable conditions the Gauss and associated anti-Gauss rules give upper and lower bounds for the value of the desired integral. It is then natural to use the average of Gauss and anti-Gauss rules as an improved approximation of the integral. Laurie also introduced these averaged rules. More recently, the author derived new averaged Gauss quadrature rules that have higher degree of exactness for the same number of nodes as the averaged rules proposed by Laurie. In [2], [5], [3] stable numerical procedures for computation of the corresponding averaged Gaussian rules are proposed. An analogous procedure can be applied also for a more general class of weighted averaged Gaussian rules introduced in [1]. Those results are presented in [4]. Here we we give a survey of the quoted results, which are obtained jointly with L. Reichel (Kent State Univ., OH (U.S.)

Computation of approximate fuel-optimal control

Iterative digital computer determination of optimal fuel control in linear time-invariant plan

On steffensen's method on Banach spaces

We present a modification of Steffensen's method as a predictor-corrector iterative method, so that we can use Steffensen's method to approximate a solution of a nonlinear equation in Banach spaces from the same starting points from which Newton's method converges. We study the semilocal convergence of the predictor-corrector method by using the majorant principle. We illustrate the method with an application to a discrete problem. © 2013 Elsevier Ltd. All rights reserved