TY - JOUR
T1 - A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration
AU - Watanabe, Yoshitaka
AU - Nakao, Mitsuhiro T.
N1 - Funding Information:
The authors heartily thank the anonymous referee for her/his thorough reading and valuable comments. This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 24340018). The computation was mainly carried out using the computer facilities at Research Institute for Information Technology,Kyushu University.
Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.
PY - 2016/3/5
Y1 - 2016/3/5
N2 - This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.
AB - This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.
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U2 - 10.1016/j.amc.2015.12.021
DO - 10.1016/j.amc.2015.12.021
M3 - Article
AN - SCOPUS:84952803254
SN - 0096-3003
VL - 276
SP - 239
EP - 251
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -