Advertisement

Introduction

  • Wolfgang Hackbusch
Chapter
  • 536 Downloads
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 120)

Abstract

We begin by recalling the following example from the analysis of ordinary differential equations. Consider the initial value problem
$$y'(x) = f\left( {x,y} \right)\,for\,x \geqslant {x_0},\;y\left( {{x_0}} \right) = {y_0}$$
(1.1.1)
Integration from x0 to x reduces this to the integral equation
$$y(x) = {y_0} + \int\limits_{{x_0}}^x {f\left( {\xi, \,y\left( \xi \right)} \right)d\xi \;for\;x \geqslant {x_0}}$$
(1.1.2)
. One reason why the reformulation (2) is of interest is because it is more suitable than (1) for proving existence and uniqueness of a solutions.

Keywords

Banach Space Quadrature Formula Interpolation Problem Quadrature Method Lipschitz Continuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielKielGermany

Personalised recommendations