ペーター・ドイフルハード

ペーター・ドイフルハードは、ドイツの数学者。専門は、数値解析。ニュートン法、常微分方程式の数値解法、偏微分方程式の数値解法に関する著書で知られている。

1. 著書
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Deuflhard, P., & Hairer, E. . Numerical treatment of inverse problems in differential and integral equations: proceedings of an international workshop, Heidelberg, Fed. Rep. of Germany, August 30-September 3, 1982 . Birkhäuser.
Deuflhard, P., & Engquist, B. . Large scale scientific computing. Birkhäuser.
Deuflhard, P., & Hohmann, A. . Numerical Analysis: A First Course in Scientific Computation. Walter de Gruyter & Co.
Deuflhard, P., & Hohmann, A. . Numerical analysis in modern scientific computing: an introduction. New York: Springer.
Deuflhard, P., & Bornemann, F., Scientific computing with ordinary differential equations. :en:Springer Science & Business Media.
Deuflhard, P. . Newton methods for nonlinear problems: affine invariance and adaptive algorithms. :en:Springer Science & Business Media.
Deuflhard, P., & Weiser, M. . Adaptive numerical solution of PDEs. Walter de Gruyter.

2. 代表的な論文
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2.1. 単著
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A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, P Deuflhard - :en:Numerische Mathematik, 1974.
Deuflhard, P. . A stepsize control for continuation methods and its special application to multiple shooting techniques. :en:Numerische Mathematik, 33, 115-146.
Deuflhard, P. . A study of extrapolation methods based on multistep schemes without parasitic solutions. Zeitschrift für Angewandte Mathematik und Physik , 30, 177-189.
Order and stepsize control in extrapolation methods, P Deuflhard - Numerische Mathematik, 1983.
Recent progress in extrapolation methods for ordinary differential equations, P Deuflhard - SIAM review, 1985.
Deuflhard, P. . Global inexact Newton methods for very large scale nonlinear problems. IMPACT of Computing in Science and Engineering, 3, 366-393.
Deuflhard, P. . Cascadic conjugate gradient methods for elliptic partial differential equations: algorithm and numerical results. Contemporary Mathematics, 180, 29-29.
Deuflhard, P. . A short history of Newton’s method. Documenta Mathematica, Optimization stories, 25-30.

2.2. 共著
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2.2.1. 1970年代
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Deuflhard, P., Pesch, H. J., & Rentrop, P. . A modified continuation method for the numerical solution of nonlinear two-point boundary value problems by shooting techniques. :en:Numerische Mathematik, 26, 327-343.
Affine invariant convergence theorems for Newton’s method and extensions to related methods, P Deuflhard, G Heindl - :en:SIAM Journal on Numerical Analysis, 1979.

2.2.2. 1980年代
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A semi-implicit mid-point rule for stiff systems of ordinary differential equations, G Bader, P Deuflhard - :en:Numerische Mathematik, 1983.
A semi-implicit mid-point rule for stiff systems of ordinary differential equations, G Bader, P Deuflhard - :en:Numerische Mathematik, 1983.
One-step and extrapolation methods for differential-algebraic systems, P Deuflhard, E Hairer, J Zugck - :en:Numerische Mathematik, 1987.
Concepts of an adaptive hierarchical finite element code, P Deuflhard, P Leinen, H Yserentant - IMPACT of Computing in Science and Engineering, 1989.

2.2.3. 1990年代
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Deuflhard, P., & Potra, F. A. . Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem. :en:SIAM Journal on Numerical Analysis, 29, 1395-1412.
Schmidt, F., & Deuflhard, P. . Discrete transparent boundary conditions for the numerical solution of Fresnel's equation. Computers & Mathematics with Applications, 29, 53-76.
The cascadic multigrid method for elliptic problems, FA Bornemann, P Deuflhard - :en:Numerische Mathematik, 1996.
Beck, R., Deuflhard, P., Hiptmair, R., Hoppe, R. H., & Wohlmuth, B. . Adaptive multilevel methods for edge element discretizations of Maxwell's equations.
A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions, P Deuflhard, HW Engl, O Scherzer - Inverse problems, 1998.
A direct approach to conformational dynamics based on hybrid Monte Carlo, C Schütte, A Fischer, W Huisinga, P Deuflhard - Journal of Computational Physics, 1999.

2.2.4. 2000年代
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Identification of almost invariant aggregates in reversible nearly uncoupled Markov chains, P Deuflhard, W Huisinga, A Fischer, C Schütte - Linear Algebra and its Applications, 2000.
Robust Perron cluster analysis in conformation dynamics, P Deuflhard, M Weber - Linear algebra and its applications, 2005.
Weiser, M., Schiela, A., & Deuflhard, P. . Asymptotic mesh independence of Newton's method revisited. :en:SIAM Journal on Numerical Analysis, 42, 1830-1845.
Franzone, P. C., Deuflhard, P., Erdmann, B., Lang, J., & Pavarino, L. F. . Adaptivity in space and time for reaction-diffusion systems in electrocardiology. :en:SIAM Journal on Scientific Computing, 28, 942-962.
Weiser, M., Deuflhard, P., & Erdmann, B. . Affine conjugate adaptive Newton methods for nonlinear elastomechanics. Optimisation Methods and Software, 22, 413-431.
Deuflhard, P., Huisinga, W., Jahnke, T., & Wulkow, M. . Adaptive discrete Galerkin methods applied to the chemical master equation. :en:SIAM Journal on Scientific Computing, 30, 2990-3011.

3. 脚注
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4. 外部リンク
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Peter Deuflhard, Emi Norris, 加古孝, [1]」『応用数理』 1994年 4巻 4号 p.377-383, 日本応用数理学会,