Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T. Some improvements of invertibility verifications for second-order linear elliptic operators. (English) Zbl 1462.65057 Appl. Numer. Math. 154, 36-46 (2020). MSC: 65J10 35J25 35J61 PDFBibTeX XMLCite \textit{Y. Watanabe} et al., Appl. Numer. Math. 154, 36--46 (2020; Zbl 1462.65057) Full Text: DOI
Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T. An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces. (English) Zbl 1506.65069 J. Differ. Equations 266, No. 9, 5431-5447 (2019). MSC: 65J10 65G20 35P15 47F05 PDFBibTeX XMLCite \textit{T. Kinoshita} et al., J. Differ. Equations 266, No. 9, 5431--5447 (2019; Zbl 1506.65069) Full Text: DOI
Nakao, Mitsuhiro T. Numerical verification for solutions to partial differential equations. (English. Japanese original) Zbl 1391.35143 Sugaku Expo. 30, No. 1, 89-109 (2017); translation from Sūgaku 65, No. 2, 113-132 (2013). MSC: 35J61 65M99 65N99 PDFBibTeX XMLCite \textit{M. T. Nakao}, Sugaku Expo. 30, No. 1, 89--109 (2017; Zbl 1391.35143); translation from Sūgaku 65, No. 2, 113--132 (2013) Full Text: DOI
Watanabe, Yoshitaka; Nakao, Mitsuhiro T. A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. (English) Zbl 1410.65228 Appl. Math. Comput. 276, 239-251 (2016). MSC: 65J15 35B25 35J40 35J91 47F05 PDFBibTeX XMLCite \textit{Y. Watanabe} and \textit{M. T. Nakao}, Appl. Math. Comput. 276, 239--251 (2016; Zbl 1410.65228) Full Text: DOI
Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T. Norm bound computation for inverses of linear operators in Hilbert spaces. (English) Zbl 1398.65094 J. Differ. Equations 260, No. 7, 6363-6374 (2016). MSC: 65G20 47F05 35P15 PDFBibTeX XMLCite \textit{Y. Watanabe} et al., J. Differ. Equations 260, No. 7, 6363--6374 (2016; Zbl 1398.65094) Full Text: DOI
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Kinoshita, Takehiko; Kimura, Takuma; Yamamoto, Nobito Some considerations of the invertibility verifications for linear elliptic operators. (English) Zbl 1320.35164 Japan J. Ind. Appl. Math. 32, No. 1, 19-31 (2015). MSC: 35J15 35P15 PDFBibTeX XMLCite \textit{M. T. Nakao} et al., Japan J. Ind. Appl. Math. 32, No. 1, 19--31 (2015; Zbl 1320.35164) Full Text: DOI
Yamamoto, Nobito; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka A theorem for numerical verification on local uniqueness of solutions to fixed-point equations. (English) Zbl 1232.47059 Numer. Funct. Anal. Optim. 32, No. 11, 1190-1204 (2011). MSC: 47N40 47H10 PDFBibTeX XMLCite \textit{N. Yamamoto} et al., Numer. Funct. Anal. Optim. 32, No. 11, 1190--1204 (2011; Zbl 1232.47059) Full Text: DOI
Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Yamamoto, Nobito; Nishida, Takaaki; Kim, Myoung-Nyoung Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems. (English) Zbl 1203.80010 J. Sci. Comput. 43, No. 3, 388-401 (2010). MSC: 80A20 76R10 65J15 65P30 PDFBibTeX XMLCite \textit{M. T. Nakao} et al., J. Sci. Comput. 43, No. 3, 388--401 (2010; Zbl 1203.80010) Full Text: DOI
Watanabe, Yoshitaka; Nakao, Mitsuhiro T. Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem. (English) Zbl 1184.65106 Japan J. Ind. Appl. Math. 26, No. 2-3, 443-463 (2009). MSC: 65N30 65C20 35B32 35J66 65N15 PDFBibTeX XMLCite \textit{Y. Watanabe} and \textit{M. T. Nakao}, Japan J. Ind. Appl. Math. 26, No. 2--3, 443--463 (2009; Zbl 1184.65106) Full Text: DOI Euclid
Kim, Myoungnyoun; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka; Nishida, Takaaki A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. (English) Zbl 1155.76024 Numer. Math. 111, No. 3, 389-406 (2009). MSC: 76E06 76M99 35Q35 PDFBibTeX XMLCite \textit{M. Kim} et al., Numer. Math. 111, No. 3, 389--406 (2009; Zbl 1155.76024) Full Text: DOI