Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
Special section on Recent Progress in Verified Numerical Computations
A simple numerical verification method for differential equations based on infinite dimensional sequential iteration
Yoshitaka Watanabe
Author information
JOURNALS FREE ACCESS

2013 Volume 4 Issue 1 Pages 23-33

Details
Abstract

This paper describes a numerical verification of solutions for infinite dimensional functional equations based on residual form and sequential iteration. Comparing with other verification procedures as typified by Newton-type iterations, the proposed algorithm can be done at low computational cost, although it needs that the formulated compact map is retractive in some neighborhood of the fixed-point to be verified. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations will be shown.

Information related to the author
© 2013 The Institute of Electronics, Information and Communication Engineers
Previous article Next article
feedback
Top