Many applications require the minimization of a smooth function f : R nu → R whose evaluation requires the solution of a system of nonlinear equations. This system represents a numerical simulation that must be run to evaluate f. This system of nonlinear equations is referred to as an implicit constraint. In principle f can be minimized using the steepest descent method or Newton-type methods f...

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface to the first edition page viii Preface to the second edition xi 1 Introduction 1 2 Parabolic equations in one space v...

After some introductory examples, this chapter considers some of the ways that delay differential equations (DDEs) differ from ordinary differential equations (ODEs). It then discusses numerical methods for DDEs and in particular, how the Runge–Kutta methods that are so popular for ODEs can be extended to DDEs. The treatment of these topics is complete, but it is necessarily brief, so it would ...

In this paper, we numerically solve a stochastic dynamic programming problem for the solution of a stochastic dynamic game for which there is a potential function. The players select a mean level of control. The state transition dynamics is a function of the current state of the system and a multiplicative noise factor on the control variables of the players. The particular application is to la...

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been prop...

In this paper, numerical solution of linear Fredholm integral equations of the second kind is considered by two methods. The methods are developed by means of the Sinc-collocation method and shifted Chebyshev polynomial method. Some numerical examples are presented to illustrate the method. Numerical solution of linear Fredholm integral equations. 1. Introduction Many initial and boundary value...

In 1798 J.-L. Lagrange published an extensive book on the solution of numerical equations. Lagrange had developed a general systematic algorithm for detecting, isolating, and approximating all real and complex roots of a polynomial equation with real coeecients, with arbitrary precision. In contrast to Newton's Method, Lagrange's algorithm is guaranteed to converge. We discuss some lesser known...

With the growing demands from disciplinary and interdisciplinary elds of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper, we examine the start-of-the-art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.