略歴: 昭和 43 年 3 月 国立佐世保工業高等専門学校機械工学科卒業 昭和 47 年 3 月 九州大学理学部数学科卒業 昭和 49 年 3 月 同上大学院理学研究科修士課程数学専攻修了 昭和 49 年 4 月 日本電信電話公社(現 NTT)横須賀電気通信研究所研究員 昭和 51 年 10 月 同上研究主任 昭和 55 年 1 月 九州大学助手(理学部) 昭和 57 年 4 月 九州工業大学講師(工学部), 59 年 10 月同助教授 昭和 63 年 10 月 九州大学助教授(理学部) 平成 6 年 6 月 九州大学教授(大学院数理学研究科, 平成 12 年 4 月より数理学研究院) 平成 14 年 7 月 九州大学大学院数理学研究院長, 大学院数理学府長(平成 18 年 7 月 15 日まで) 平成 19 年 4 月 九州大学産業技術数理研究センター長 平成 21 年 5 月 九州大学主幹教授 平成 22 年 4 月 佐世保工業高等専門学校長 九州大学名誉教授 学位: 昭和 59 年 4 月 理学博士(九州大学) 専門分野: 計算数学 研究テーマ: 偏微分方程式の解に対する数値的検証法の研究 有限要素法の構成的誤差評価 数値計算の信頼性 研究内容キーワード: 事後誤差評価 精度保証付き数値計算法 計算機援用解析学 非線形現象 1 所属学協会: ・ 日本数学会 ・ 日本応用数理学会 ・ 情報処理学会 ・ 日本計算工学会 ・ 統計科学研究会 ・日本工学教育協会 受賞: 平成 19 年 12 月 「ナイスステップな研究者」選定(文部科学省科学技術政策研究所) 平成 23 年 9 月 日本応用数理学会論文賞(JJIAM 部門) 平成 24 年 9 月 日本数学会賞秋季賞 平成 26 年 4 月 文部科学大臣表彰科学技術賞(研究部門) 科学研究費の取得状況: [1] 基盤研究 (C)、平成 24-26 年度、「非線形発展方程式の解に対する精度保証付き数値 計算法」、代表、3,900(千円) [2] 基盤研究 (S)、平成 20-23 年度、 「非線形現象解明に向けた計算機援用解析学の構築」、 代表、65,300(千円) [3] 萌芽研究、平成 17-19 年度、「数値処理と数式処理の融合による計算機援用解析学の 可能性に関する基礎的研究」、代表、3,300(千円) [4] 基盤研究 (A)(1)(一般)、平成 15-18 年度、「数値的検証法から計算機援用解析学の 構築へ向けての総合的研究」、代表、24,800(千円) [5] 基盤研究 (B)(1)(一般)、平成 13-14 年度、「精度保証付き数値計算法の新展開を目 ざしての総合的研究」、代表、17,000(千円) [6] 基盤研究 (B)(1)(一般)、平成 10-11 年度、「精度保証付き数値計算とその計算理工 学への応用に関する総合的研究」、代表、11,900(千円) [7] 基盤研究 (A)(1)(一般)、平成 8-9 年度、「新しい科学計算技法と応用解析の総合的 研究」、代表、9,400(千円) 2 主な研究業績: [1] 河岡、友永(中尾の旧姓)、高橋,通信制御プログラムに関するプロトコル試験手順 の最適化,電子通信学会論文誌,J63-D,8 (1980),618-625. [2] Nakao, M., Some superconvergence estimates for a collocation-H −1 -Galerkin method for parabolic problems, Memoirs of Faculty of Science Kyushu University, Ser. A 35 (1981), 291-306. [3] Tomonaga(中尾の旧姓), M., Optimal error estimates for H −1 -Galerkin method for parabolic problems with time dependent coefficients, Memoirs of Numerical Mathematics No. 8/9 (1982), 65-85. [4] Nakao, M., Collocation-H −1 -Galerkin method for some parabolic equations in two space variables, Memoirs of Faculty of Science Kyushu University, Ser. A 36 (1982), 129-143. [5] Nakao, M., Interior estimates and superconvergence for H −1 -Galerkin method to elliptic equations, Bulletin of the Kyushu Institute of Technology (Math. & Natur. Sci.) 30 (1983), 19-30. [6] Nakao, M., Superconvergence estimates at Jacobi points of the collocation-Galerkin method for two point boundary value problems, Journal of Information Processing, 7 (1984), 31-34. [7] Nakao, M., Some superconvergence estimates for a Galerkin method for elliptic problems, Bulletin of the Kyushu Institute of Technology (Math. & Natur. Sci.) 31 (1984), 49-58. [8] Nakao, M., A collocation-H −1 -Galerkin method for some elliptic equations, Mathematics of Computation 42 (1984), 417-426. [9] Nakao, M.T., L∞ error estimates and superconvergence results for a collocationH −1 -Galerkin method for elliptic equations, Memoirs of Faculty of Science Kyushu University, Ser. A 39 (1985), 1-25. [10] Nakao, M., Some superconvergence of Galerkin approximations for parabolic and hyperbolic problems in one space dimension, Bulletin of the Kyushu Institute of Technology (Math. & Natur. Sci.) 32 (1985), 1-14. [11] Nakao, M.T., Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension, Numerische Mathematik 47 (1985), 139-157. [12] Nakao, M.T., Some superconvergence for a Galerkin method by averaging gradients in one dimensional problems, Journal of Information Processing, 9 (1986), 130-134. 3 [13] Nakao, M.T., Superconvergence of gradients of Galerkin approximations for elliptic problems, Mathematical Modelling and Numerical Analysis 21 (1987), 679-695. [14] Nakao, M.T., A numerical approach to the proof of existence of solutions for elliptic problems, Japan Journal of Applied Mathematics 5 (1988), 313-332. [15] Nakao, M.T., A computational verification method of existence of solutions for nonlinear elliptic equations, Lecture Notes in Num. Appl. Anal., 10, (1989) 101 - 120. In proc. Recent Topics in Nonlinear PDE 4, Kyoto, 1988, N orth − Holland/Kinokuniya, 1989. [16] Nakao, M.T., A numerical approach to the proof of existence of solutions for elliptic problems I I, Japan Journal of Applied Mathematics 7 (1990), 477-488. [17] Nakao, M.T. & Yamamoto, N., Numerical verifications of solutions for elliptic equations with strong nonlinearity, Numerical Functional Analysis and Optimization 12 (1991), 535-543. [18] Nakao, M.T., Solving nonlinear parabolic problems with result verification Part I: One space dimensional case, Journal of Computational and Applied Mathematics 38 (1991) 323-334. [19] Nakao, M.T., A numerical verification method for the existence of weak solutions for nonlinear boundary value problems, Journal of Mathematical Analysis and Applications 164 (1992), 489-507. [20] Nakao, M.T., Computable error estimates for FEM and numerical verification of solutions for nonlinear PDEs, Computational and Applied Mathematics, I (eds. C.Brezinski and U.Kulisch), North-Holland (1992), 357-366 . [21] Watanabe, Y. & Nakao, M.T., Numerical verifications of solutions for nonlinear elliptic equations, Japan Journal of Industrial and Applied Mathematics 10 (1993), 165-178. [22] Nakao, M.T., Solving nonlinear elliptic problems with result verification using an H −1 residual iteration, Computing, Supplementum 9 (1993), 161-173. [23] Nakao, M.T., Computable L∞ error estimates in the finite element method with application to nonlinear elliptic problems, Series in Applicable Analysis Vol.2, Contributions in Numerical Mathematics(ed. R.P. Agarwal), World Scientific (1993), 309-319. [24] Yamamoto, N. & Nakao, M.T., Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains, Numerische Mathematik 65 (1993), 503-521. 4 [25] Nakao, M.T. & Watanabe, Y., On computational proofs of the existence of solutions to nonlinear parabolic problems, Journal of Computational and Applied Mathematics 50 (1994), 401-410. [26] Nakao, M.T., Numerical verifications of solutions for nonlinear hyperbolic equations, Interval Computations 4 (1994), 64-77. [27] Yamamoto, N. & Nakao, M.T., Numerical verifications for solutions to elliptic equations using residual iterations with higher order finite element, Journal of Computational and Applied Mathematics 60 (1995), 271-279. [28] Nakao, M.T. & Yamamoto, N., A simplified method of numerical verification for nonlinear elliptic equations, in the Proceedings of International Symposium on Nonlinear Theory and its Applications (NOLTA’95), Las Vegas, USA, (1995), 263266. [29] Nakao, M.T., Yamamoto, N. & Watanabe, Y., Guaranteed error bounds for finite element solutions of the Stokes problem, in Scientific Computing and Validated Numerics (G. Alefeld et al. eds.), Akademie Verlag, Berlin (1996), 258-264. [30] Watanabe, Y., Nakao, M.T. & Yamamoto, N., Verified computation of solutions for nondifferentiable elliptic equations related to MHD equilibria, Nonlinear Analysis, Theory, Methods and Applications 28, (1997), 577-587. [31] Tsuchiya, T. & Nakao, M.T., Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points, Japan Journal of Industrial and Applied Mathematics 14 (1997), 357-372. [32] Minamoto, T. & Nakao, M.T., Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case, Reliable Computing 3, (1997), 137-147. [33] Nakao, M.T. & Yamamoto, N., Numerical verification of solutions for nonlinear elliptic problems using L∞ residual method, Journal of Mathematical Analysis and Applications 217, (1998), 246-262. [34] Nakao, M.T., Yamamoto, N. & Kimura, S., On best constant in the optimal error stimates for the H01 -projection into piecewise polynomial spaces, Journal of Approximation Theory 93, (1998), 491-500. [35] Nakao, M.T., Yamamoto, N. & Watanabe, Y., Constructive L2 error estimates for finite element solutions of the Stokes equations, Reliable Computing 4 (1998), 115-124. [36] Nakao, M.T., Yamamoto, N. & Watanabe, Y., A posteriori and constructive a priori error bounds for finite element solutions of Stokes equations, Journal of Computational and Applied Mathematics 91(1998), 137-158. 5 [37] Nakao, M.T., Yamamoto, N. & Nishimura, Y., Numerical verification of the solution curve for some parametrized nonlinear elliptic problem, in Proc. Third China-Japan Seminar on Numerical Matehmatics, Aug. 26-30, Dalian, China, 1996 (eds. Shi, Z.-C. & Mori, M.), Science Press, Beijing , (1998), 238-245. [38] Ryoo, C-S & Nakao, M.T., Numerical verification of solutions for variational inequalities, Numerische Mathematik 81 (1998), 305-320. [39] Nakao, M.T. & Ryoo, C-S, Numerical verifications of solutions for variational inequalities using Newton-like Method, INFORMATION, 2 (1999), 27-35. [40] Nakao, M.T., Yamamoto, N. & Nagatou, K., Numerical verifications of eigenvalues of second-order elliptic operators, Japan Journal of Industrial and Applied Mathematics 16 (1999), 307-320. [41] Nagatou, K., Yamamoto, N. & Nakao, M.T., An approach to the numerical verification of solutions for nonlinear elliptic problems with local uniqueness, Numerical Functional Analysis and Optimization 20 (1999), 543-565. [42] Watanabe, Y., Yamamoto, N. & Nakao, M.T., A numerical verification method of solutions for the Navier-Stokes equations, Reliable Computing 5 (1999), 347-357. [43] Yamamoto, N., Nakao, M.T. & Watanabe, Y., Validated computation for a linear elliptic problem with a parameter, GAKUTO International Series, Mathematical Sciences and Applications Vol. 12 (eds. Kawarada et al.), Advances in Numerical Mathematics ; Proc. Fourth Japan-China Joint Seminar on Numerical Mtahematics, Aug. 24-28, 1998, Chiba, Japan, (1999), 155-162. [44] Watanabe, Y., Yamamoto, N. & Nakao, M.T., Verification method of generalized eigenvalue problems and its applications(in Japanese), Transaction of the Japan Society for Industrial and Applied Mathematics, Vol. 9 No. 3 (1999), 137-150. [45] Nakao, M.T., Lee, S.H. & Ryoo, C.S., Numerical verification of solutions for elastoplastic torsion problems, Computers & Mathematics with Applications 39 (2000), 195-204. [46] Minamoto, T., Yamamoto, N. & Nakao, M.T., Numerical verification method for solutions of the perturbed Gelfand equation, Methods and Applications of Analysis 7 (2000), 251-262. [47] Toyonaga, K. & Nakao, M.T., Numerical enclosure for the optimal threshold probability in discounted Markov decision processes, Bulletin of Informatics and Cybernetics, 32 (2000), 81-90. [48] Nagatou, K. & Nakao, M.T., An enclosure method of eigenvalues for the elliptic operator linearlized at an exact solution of nonlinear problems, Linear Algebra and its Applications 324 (2001), 81-106. 6 [49] Nakao, M.T., Watanabe, Y. & Yamamoto, N., Verified numerical computations for an inverse elliptic eigenvalue problem with finite data, Japan Journal of Industrial and Applied Mathematics 18 (2001), 587-602. [50] Nakao, M.T. & Yamamoto, N., A guaranteed bound of the optimal constant in the error estimates for linear triangular element, Computing Supplementum 15 (2001), 165-173. [51] Nakao, M.T. & Yamamoto, N., A guaranteed bound of the optimal constant in the error estimates for linear triangular element Part : Details, Perspectives on Enclosure Methods (eds. U. Kulisch et al.), the Proceedings Volume for Invited Lectures of SCAN2000, Springer-Verlag, Vienna (2001), 265-276. [52] M.T. Nakao & C-S Ryoo, Numerical verification methods for solutions of free boundary problems, the Proceedings of MSCOM(International Symposium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics), Sept. 29-Oct. 3, 2000, Yamaguchi, Japan (Miyoshi et al. eds.), Lecture Notes in Computational Science and Engineering, Springer Verlag (2001), 195-208. [53] Nakao, M.T. & Toyonaga, K., An improvement of the enclosure method for elliptic eigenvalue problems, in the Proceedings of Fifth China-Japan Seminar on Numerical Matehmatics, Aug. 21-25, 2000, Shanghai, China (eds. Shi, Z.-C. & Kawarada, H.), Science Press, Beijing (2002), 181-188. [54] Ryoo, C-S & Nakao, M.T., Numerical verification of solutions for variational inequalities of the Second Kind, Computer and Mathematics with Applications 43 (2002), 1371-1380. [55] Toyonaga, K., Nakao, M.T. & Watanabe, Y., Verified numerical computations for multiple or nearly multiple eigenvalues for elliptic operators, Journal of Computational and Applied Mathematics 147 (2002) 175-190. [56] Nagatou, K., Nakao, M.T. & Wakayama, M., Verified numerical computations for eigenvalues of non-commutative harmonic oscillators, Numerical Functional Analysis and Optimization 23 (2002), 633-650. [57] Nakao, M.T., Watanabe, Y., Yamamoto, N. & Nishida, T., Some computer assisted proofs for solutions of the heat convection problems, Reliable Computing 9 (2003), 359-372. [58] Ryoo, C-S & Nakao, M.T., Numerical verification of solutions for obstacle problems, Journal of Computational and Applied Mathematics 161 (2003), 405-416. [59] Y. Watanabe, N. Yamamoto, M. T. Nakao & T. Nishida, A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem, Journal of Mathematical Fluid Mechanics 6 (2004), 1-20. 7 [60] Nakao, M.T. & Watanabe, Y., An efficient approach to the numerical verification for solutions of elliptic differential equations, Numerical Algorithms 37, Special issue for Proceedings of SCAN2002 (2004), 311-323. [61] Hashimoto, K., Abe, R., Nakao, M.T. & Watanabe, Y., A Numerical Verification Method for Solutions of Singularly Perturbed Problems with Nonlinearity, Japan Journal of Industrial and Applied Mathematics 22 (2005), 111-131 [62] Nakao, M.T., Hashimoto, K. & Watanabe, Y., A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems, Computing 75 (2005), 1-14. [63] Hashimoto, K., Kobayashi, K. & Nakao, M.T., Numerical Verification Methods of Solutions for the Free Boundary Problems, Numerical Functional Analysis and Optimization 26 (2005), 523-542. [64] Watanabe, Y., Yamamoto, N. & Nakao, M.T., An efficient approach to numerical verification for solutions of elliptic differential equations with local uniqueness(in Japanese), Transaction of the Japan Society for Industrial and Applied Mathematics, Vol.15, No.4 (2005), 509-520. [65] M. T. Nakao, Y. Watanabe, N. Yamamoto & T. Nishida, A numerical verification of bifurcation points for nonlinear heat convection problems, in the proceedings of 2nd International Conference ”From Scientific Computing to Computational Engineering”, Athen, 5-8 July, 2006, 8 pages. [66] M.-N. Kim, M.T. Nakao, Y. Watanabe & T. Nishida, Some computer assisted proofs on three dimensional heat convection problems, in Proceedings of Nonlinear Theory and its Applications NOLTA 2006, 11-14 September, Bologna, Italy (2006), 427-430. [67] Nagatou, K., Hashimoto, K, Nakao, M.T., Numerical verification of stationary solutions for Navier-Stokes problems, Journal of Computational and Applied Mathematics 199 (2007), 424-431. [68] Minamoto, T. and Nakao, M.T., Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation, Journal of Computational and Applied Mathematics 202 (2007), 177-185. [69] Nakao, M.T., Hashimoto, K., Kobayashi, K., Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains, Hokkaido Mathematical Journal, Vol. 36, Special Issue, Proceedings on ”The First China-Japan-Korea Joint Conference on Numerical Mathematics” (2007), 777-799. 8 [70] Nakao, M.T., Hashimoto, K., Nagatou, K., A computational approach to constructive a priori and a posteriori error estimates for finite element approximations of bi-harmonic problems, GAKUTO International Series, Mathematical Sciences and Applications Vol. 28, Proceedings of the 4th JSIAM-SIMAI Seminar on Industrial and Applied Mathematics, May 26-28, 2005, Hayama, Japan (2008), 139-148. [71] Nakao, M.T., Hashimoto, K., Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications, Journal of Computational and Applied Mathematics, 218 (2008), 106-115. [72] Nakao, M.T., Kinoshita, T., Some remarks on the behaviour of the finite element solution in nonsmooth domains, Applied Mathematics Letters 21 (2008), 13101314. [73] M.-N. Kim, M.T. Nakao, Y. Watanabe, T. Nishida, A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-B´enard problems, Numerische Mathematik 111 (2009), 389-406. [74] Nakao, M.T., Kinoshita, T., On very accurate verification of solutions for boundary value problems by using spectral methods, JSIAM Letters 1(2009), 21-24. [75] Kinoshita, T., Hashimoto, K. and Nakao, M.T., On the L2 a priori error estimates to the finite element solution of elliptic problems with singular adjoint operator, Numerical Functional Analysis and Optimization 30 (2009), 289-305. [76] Watanabe, Y., Plum, M, Nakao, M.T., A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow, Zeitschrift fuer Angewandte Mathematik und Mechanik(ZAMM) 89 (2009), 5-18 [77] M.T. Nakao, Y. Watanabe, N. Yamamoto, T. Nishida, M.-N. Kim, Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems, Journal of Scientific Computing Vol.43, No. 3 (2010), 388-401, Proc. International Conference on Recent Developments of Numerical Schemes for Flow Problems(INSF2007, Fukuoka, Japan). [78] Nakao, M.T. and Hashimoto, K., A numerical verification method for solutions of nonlinear parabolic problems, Journal of Math-for-Industry, JMI2009A-9 (2009), 69-72. [79] Y. Watanabe, M. T. Nakao, Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-B´enard problem, Japan Journal of Industrial and Applied Mathematics, 26 (2009), 443-463. [80] T. Kinoshita, M. T. Nakao, On very accurate enclosure ofthe optimal constant in the a priori error estimates for H02 -projection, Journal of Computational and Applied Mathematics 234 (2010), 526-537. 9 [81] T. Minamoto, M. T. Nakao, A numerical verification method for a periodic solution of a delay differential equation, Journal of Computational and Applied Mathematics 235 (2010), 870-878. [82] M. T. Nakao,Y. Watanabe, Numerical Verification Methods for Solutions of Semilinear Elliptic Boundary Value Problems, Nonlinear Theory and Its Applications, IEICE, 2 (2011), 2-31. [83] Y. Watanabe, K. Nagatou, M. Plum, M. T. Nakao, A Computer-assisted Stability Proof for the Orr-Sommerfeld Problem with Poiseuille Flow, Nonlinear Theory and Its Applications, IEICE, 2 (2011), 123-127. [84] N. Yamamoto, M.T. Nakao, Y. Watanabe, A theorem for numerical verification on local uniqueness of solutions to fixed-point equations, Numerical Functional Analysis and Optimization, 32 (2011), 1190-1204. [85] T. Kinoshita, T. Kimura, M.T. Nakao, A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations, Journal of Computational and Applied Mathematics, 236 (2011), 1622-1636. [86] M. T. Nakao, T. Kinoshita, T. Kimura, On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems, Computing 94 (2012), 151-162. [87] K. Nagatou, M. Plum, M. T. Nakao, Eigenvalue excluding for perturbed-periodic one-dimensional Schr¨odinger operators, Proceedings of the Royal Society London Series A Math. Phy. Eng. Sci. 468 (2012), 545-562. doi:10.1098/rspa.2011.0159. [88] T. Kimura, T. Kinoshita, M.T. Nakao, Some remarks on the instability of approximate solutions for ODEs, Nonlinear Theory and Its Applications, IEICE Vol. 4 No. 1 (2013), 80-87. DOI:10.1588/nolta.4.80. [89] Y. Watanabe, T. Kinoshita, M.T. Nakao, A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations, Mathematics of Computation, 82 (2013), 1543-1557. DOI:10.1090/S0025-57182013-02676-2 [90] M. T. Nakao, T. Kimura, T. Kinoshita, Constructive a priori error estimates for a full discrete approximation of the heat equation, SIAM Journal on Numerial Analysis, 51 (2013), 1525-1541. DOI:10.1137/120875661 [91] T. Kinoshita1, Y. Watanabe, M. T. Nakao, An improvement of the theorem of a posteriori estimates for inverse elliptic operators, Nonlinear Theory and Its Applications, IEICE Vol. 5 No. 1 (2014), 47-52. DOI:10.1587/nolta.5.47 10 [92] T. Kinoshita, T. Kimura, M. T. Nakao, On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems, Numerische Mathematik, 126 (2014), 679-701. open access, DOI 10.1007/s00211-013-0575-z. [93] Y. Watanabe, K. Nagatou, M. Plum, M. T. Nakao, Verified computations of eigenvalue exclosures for eigenvalue problems in Hilbert spaces, to appear in SIAM Journal on Numerial Analysis. [解説論文] [1] 河岡、友永(中尾の旧姓)、高橋,プロトコルの記述法と検証法、情報処理、20巻 7号 (1979), 612-621. [2] 中尾充宏、関数方程式の解の存在に対する数値的検証法、数学、42 (1990),16-31. (英 訳版:Numerical verification methods for the existence of solutions for functional equations, Sugaku Exposition 5 (1992), 71-91.) [3] 中尾充宏、精度保証付き数値計算の現状と動向、情報処理、31巻9号 (1990), 11771190. [4] Mitsuhiro T. Nakao, State of the art for numerical computations with guaranteed accuracy, Mathematica Japonica, Vol. 48, No.2 (1997), 323-338. [5] 中尾充宏、精度保証による数値解析、数理科学、No. 417 (1998), 28-34. [6] 渡部善隆、中尾充宏、偏微分方程式の精度保証、シミュレーション、19巻3号 (2000), 208-215. [7] Nakao, M.T., Numerical verification methods for solutions of ordinary and partial differential equations, Numerical Functional Analysis and Optimization 22(3&4) (2001), 321-356. [8] 中尾充宏、偏微分方程式の解に対する数値的存在検証—研究の原点とその展開—、 Fundamentals Review Vol.2 No.3、電子情報通信学会、基礎・境界ソサイエティ、 (2008), 19-28. [9] 中尾充宏、精度保証付き数値計算の応用:流体の方程式、数学セミナー、Vol. 47, No.11 (2008), 24-30. [10] 中尾充宏、数値計算の信頼性評価―コンピュータを使った新しい解析学、応用数理 Vol.21、No.2(2011), 61-66. [11] 中尾充宏、流体力学における精度保証付き数値計算, 数理科学, No. 578 (2011), 26-32. [12] 中尾充宏、小特集「数値シミュレーションの品質保証」(総括)、シミュレーション、 31 巻 3 号 (2012), 133-135. 11 [13] 中尾充宏、偏微分方程式の解に対する精度保証付き数値計算、数学、65 (2013), 113132. [著書] [1] 中尾充宏・山本野人,「精度保証付き数値計算」, 日本評論社, 1998. [2] Alefeld, G., Nakao, M.T., and Rump, S. (Guest Editors), Special Issue: Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004), Journal of Computational and Applied Mathematics 199/2 (2007), 453 pages. [3] 中尾充宏 (分担執筆), 数学辞典 (第 4 版), 岩波書店, 東京, 2007. [4] 田端正久・中尾充宏, 偏微分方程式から数値シミュレーションへ/計算の信頼性評価, 現代技術への数学入門シリーズ, 講談社, 東京, 2008. (分担頁:63-120) [5] Nakao, M.T., and Oishi, S.(Guest Editors), Special Issue: State of the Art for Self-Validating Numerical Computations, Japan Journal of Industrial and Applied Mathematics 26-2/3 (2009), 411 pages. 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