TY - JOUR
T1 - Numerical verification methods for solutions of ordinary and partial differential equations
AU - Nakao, M. T.
PY - 2001/5
Y1 - 2001/5
N2 - In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.
AB - In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.
KW - Computer assisted proof in analysis
KW - Nonlinear differential equation
KW - Numerical verification
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U2 - 10.1081/NFA-100105107
DO - 10.1081/NFA-100105107
M3 - Article
AN - SCOPUS:0035326665
SN - 0163-0563
VL - 22
SP - 321
EP - 356
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 3-4
ER -