Hashimoto, Kouji; Kinoshita, Takehiko; Nakao, Mitsuhiro T. Numerical verification of solutions for nonlinear parabolic problems. (English) Zbl 1450.65121 Numer. Funct. Anal. Optim. 41, No. 12, 1495-1514 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 65M15 35K55 35K05 PDFBibTeX XMLCite \textit{K. Hashimoto} et al., Numer. Funct. Anal. Optim. 41, No. 12, 1495--1514 (2020; Zbl 1450.65121) Full Text: DOI arXiv
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
Kinoshita, T.; Hashimoto, K.; Nakao, M. T. On the \(L^{2}\) a priori error estimates to the finite element solution of elliptic problems with singular adjoint operator. (English) Zbl 1165.35009 Numer. Funct. Anal. Optim. 30, No. 3-4, 289-305 (2009). MSC: 35J25 65N15 65N30 65G99 PDFBibTeX XMLCite \textit{T. Kinoshita} et al., Numer. Funct. Anal. Optim. 30, No. 3--4, 289--305 (2009; Zbl 1165.35009) Full Text: DOI Link
Hashimoto, Kouji; Kobayashi, Kenta; Nakao, Mitsuhiro T. Numerical verification methods for solutions of the free boundary problem. (English) Zbl 1081.65081 Numer. Funct. Anal. Optimization 26, No. 4-5, 523-542 (2005). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L60 65L10 34B15 65G20 PDFBibTeX XMLCite \textit{K. Hashimoto} et al., Numer. Funct. Anal. Optim. 26, No. 4--5, 523--542 (2005; Zbl 1081.65081) Full Text: DOI Link
Nagatou, K.; Nakao, M. T.; Wakayama, M. Verified numerical computations for eigenvalues of non-commutative harmonic oscillators. (English) Zbl 1016.65056 Numer. Funct. Anal. Optimization 23, No. 5-6, 633-650 (2002). Reviewer: Oscar Lopez-Pouso (Santiago de Compostela) MSC: 65L15 47N50 81Q05 65G20 65G40 34L16 34L40 47E05 PDFBibTeX XMLCite \textit{K. Nagatou} et al., Numer. Funct. Anal. Optim. 23, No. 5--6, 633--650 (2002; Zbl 1016.65056) Full Text: DOI
Nakao, Mitsuhiro T. Numerical verification methods for solutions of ordinary and partial differential equations. (English) Zbl 1106.65315 Numer. Funct. Anal. Optimization 22, No. 3-4, 321-356 (2001). MSC: 65G20 PDFBibTeX XMLCite \textit{M. T. Nakao}, Numer. Funct. Anal. Optim. 22, No. 3--4, 321--356 (2001; Zbl 1106.65315) Full Text: DOI
Nagatou, K.; Yamamoto, N.; Nakao, M. T. An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness. (English) Zbl 0938.65137 Numer. Funct. Anal. Optimization 20, No. 5-6, 543-565 (1999). Reviewer: Isaac Yevzerov (Kyïv) MSC: 65N30 35J60 65G20 PDFBibTeX XMLCite \textit{K. Nagatou} et al., Numer. Funct. Anal. Optim. 20, No. 5--6, 543--565 (1999; Zbl 0938.65137) Full Text: DOI
Nakao, Mitsuhiro T.; Yamamoto, Nobito Numerical verifications of solutions for elliptic equations with strong nonlinearity. (English) Zbl 0746.35014 Numer. Funct. Anal. Optimization 12, No. 5-6, 535-544 (1991). MSC: 35J65 65N15 68T15 35D05 35-04 PDFBibTeX XMLCite \textit{M. T. Nakao} and \textit{N. Yamamoto}, Numer. Funct. Anal. Optim. 12, No. 5--6, 535--544 (1991; Zbl 0746.35014) Full Text: DOI