On the epistemological analysis of modeling and computational error in the mathematical sciences

[1]  Barry N. Taylor,et al.  Guidelines for Evaluating and Expressing the Uncertainty of Nist Measurement Results , 2017 .

[2]  Robert M. Corless,et al.  A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis , 2013 .

[3]  Wendy S. Parker,et al.  Computer simulation and philosophy of science , 2012 .

[4]  Christopher Pincock,et al.  Mathematics and Scientific Representation , 2012 .

[5]  Wendy S. Parker,et al.  An Instrument for What? Digital Computers, Simulation and Scientific Practice , 2010 .

[6]  Paul Humphreys,et al.  The philosophical novelty of computer simulation methods , 2009, Synthese.

[7]  Cyrille Imbert,et al.  Computer simulations as experiments , 2009, Synthese.

[8]  Margaret Morrison,et al.  Models, measurement and computer simulation: the changing face of experimentation , 2009 .

[9]  Penelope Maddy,et al.  The logical structure of the world , 2007 .

[10]  T. Trucano,et al.  Verification, Validation, and Predictive Capability in Computational Engineering and Physics , 2004 .

[11]  A. Hohmann,et al.  Numerical Analysis in Modern Scientific Computing: An Introduction , 2003 .

[12]  John Earman,et al.  CETERIS PARIBUS LOST , 2002 .

[13]  Robert W. Batterman,et al.  Asymptotics and the Role of Minimal Models , 2002, The British Journal for the Philosophy of Science.

[14]  Sheldon R. Smith,et al.  Violated Laws, Ceteris Paribus Clauses, and Capacities , 2002, Synthese.

[15]  Sheldon R. Smith Models and the Unity of Classical Physics: Nancy Cartwright's Dappled World , 2001, Philosophy of Science.

[16]  Patrick Knupp,et al.  Code Verification by the Method of Manufactured Solutions , 2000 .

[17]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[18]  Kevin T. Kelly The Logic of Reliable Inquiry , 1996 .

[19]  Lloyd N. Trefethen,et al.  The Definition of Numerical Analysis , 1992 .

[20]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[21]  P. Zweifel Advanced Mathematical Methods for Scientists and Engineers , 1980 .

[22]  H. Putnam Mathematics, Matter and Method: The ‘corroboration’ of theories , 1979 .

[23]  J. H. Wilkinson Modern Error Analysis , 1971 .

[24]  S. Toulmin,et al.  Philosophy of Science , 1970, The British Journal for the History of Science.

[25]  A. M. Turing,et al.  Computing Machinery and Intelligence , 1950, The Philosophy of Artificial Intelligence.

[26]  W F SHAW,et al.  The Scientific Outlook , 1948, Nature.

[27]  J. Neumann,et al.  Numerical inverting of matrices of high order , 1947 .

[28]  H. Reichenbach Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge , 1938 .

[29]  Pierre Maurice Marie Duhem,et al.  La théorie physique. Son objet, sa structure , 1906 .

[30]  Nicolas Fillion,et al.  The Reasonable Effectiveness of Mathematics in the Natural Sciences , 2012 .

[31]  Nicolas Fillion,et al.  Backward Error Analysis as a Model of Computation for Numerical Methods , 2011 .

[32]  Mark A. Wilson,et al.  Wandering significance : an essay on conceptual behavior , 2006 .

[33]  Paul Humphreys,et al.  Extending Ourselves: Computational Science, Empiricism, and Scientific Method , 2004 .

[34]  Peter Deuflhard,et al.  Numerical Analysis in Modern Scientific Computing , 2003 .

[35]  Robert W. Batterman,et al.  The devil in the details : asymptotic reasoning in explanation, reduction, and emergence , 2002 .

[36]  S. Orszag,et al.  Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory. , 1999 .

[37]  Routledge,et al.  Routledge Encyclopedia of Philosophy , 1998 .

[38]  Stephan Hartmann,et al.  The World as a Process: Simulations in the Natural and Social Sciences , 1996 .

[39]  Stephan Hartmann,et al.  The World as a Process , 1996 .

[40]  Klaus G. Troitzsch,et al.  Modelling and simulation in the social sciences from the philosophy of science point of view , 1996 .

[41]  Howard Stein,et al.  Some reflections on the structure of our knowledge in physics , 1995 .

[42]  E. Iso,et al.  Measurement Uncertainty and Probability: Guide to the Expression of Uncertainty in Measurement , 1995 .

[43]  P. Duhem,et al.  La Th'eorie Physique: son Object et sa Structure , 1991 .

[44]  Wang Qiu-Dong,et al.  The global solution of the N-body problem , 1990 .

[45]  P. Thagard,et al.  Computational Philosophy of Science , 1988 .

[46]  Roger H. Stuewer,et al.  Historical and philosophical perspectives of science , 1970 .

[47]  J. Miller Numerical Analysis , 1966, Nature.