The Online Books Page

Differential equations, Partial -- Numerical solutions

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• Differential equations, Partial
• Numerical analysis
• Differential equations -- Numerical solutions

• Maximum principles (Mathematics)

• Homogeneous Boltzmann Equation in Quantum Relativistic Kinetic Theory (EJDE monograph #4, 2003), by Miguel Escobedo, Stéphane Mischler, and Manuel A. Valle (PDF with commentary at ams.org)

Items below (if any) are from related and broader terms.

• The Hopf Bifurcation and Its Applications (1976), by Jerrold E. Marsden and Marjorie McCracken (PDF files at Caltech)
• Differential Systems (American Mathematical Society Colloquium Publications v21; 1937), by Joseph Miller Thomas (multiple formats at archive.org)
• Hilbert Space Methods for Partial Differential Equations, by R. E. Showalter (PDF files at ams.org)
• Partielle Differentialgleichungen der Physik (2 manuscript volumes in German; ca. 1888), by Felix Klein (page images at HathiTrust)
• Analog Simulation: Solution of Field Problems (New York et al.: McGraw-Hill Book Co., 1958), by Walter J. Karplus (page images at HathiTrust)

• Solving PDEs in Python: The FEniCS Tutorial I (Simula SpringerBriefs on Computing v3; Cham: Springer Open, c2016), by Hans Petter Langtangen and Anders Logg (PDF with commentary at Springer)

• Dynamics of Partial Differential Equations (2004-; all articles more than about 4 years old, and some later articles, free to read) (partial serial archives)

• Mémoire sur le Problème d'Analyse Relatif à l'Équilibre des Plaques Élastiques Encastrées (in French; Paris: Imprimerie Nationale, 1909), by Jacques Hadamard (page images at HathiTrust; US access only)

• Existence, Multiplicity, Perturbation, and Concentration Results for a Class of Quasi-Linear Elliptic Problems (EJDE monograph #7, 2006), by Marco Squassina (PDF with commentary at ams.org)
• Palais-Smale Approaches to Semilinear Elliptic Equations in Unbounded Domains (EJDE monograph #6, 2004), by Hwai-chiuan Wang (PDF with commentary at ams.org)

• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (1984), by Peter B. Gilkey (Postscript files at emis.de)

• Spheroidal Wave Functions (Stanford: Stanford University Press, 1957), by Carson Flammer (page images at HathiTrust)

• Fundamental Numerical Methods and Data Analysis (c2003), by George W. Collins (PDF files at Harvard)
• Sketch of the Analytical Engine Invented by Charles Babbage, Esq., With Notes Upon the Memoir, by Luigi Federico Menabrea and Ada King Lovelace
  • illustrated HTML at Fourmilab
  • Gutenberg illustrated HTML

• Numerical Recipes in C: The Art of Scientific Computing (second edition, 1992), by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery (FileOpen-dependent PDF files at nrbook.com)
• Numerical Recipes in FORTRAN: The Art of Scientific Computing (second edition, 1992), by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery (FileOpen-dependent PDF files at nrbook.com)

• Numerical Computing With MATLAB (2013), by Cleve B. Moler (PDF files with commentary at mathworks.com)

• Solving PDEs in Python: The FEniCS Tutorial I (Simula SpringerBriefs on Computing v3; Cham: Springer Open, c2016), by Hans Petter Langtangen and Anders Logg (PDF with commentary at Springer)

• Electronic Transactions on Numerical Analysis (1993-) (full serial archives)
• SMAI Journal of Computational Mathematics (2015-) (full serial archives)
• Annales de l'Institut Henri Poincaré: Analyse Non Linéaire (in French) (partial serial archives)
• ESAIM: Mathematical Modelling and Numerical Analysis (partial serial archives)

• Electronic Journal of Boundary Elements (2003-) (full serial archives)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)

• Discrete Mathematics: An Open Introduction (third edition, 2020), by Oscar Levin (illustrated HTML and PDF with commentary at openmathbooks.org)

• A Cool Brisk Walk Through Discrete Mathematics (c2023), by Stephen Davies (PDF with commentary at allthemath.org)

• Feedback Systems: An Introduction for Scientists and Engineers (Princeton and Oxford: Princeton University Press, c2008), by Karl J. Åström and Richard M. Murray (PDF at Caltech)
• Fundamental Limitations in Filtering and Control (c1997; errata corrected 2004), by M. Seron, J. Braslavsky, and Graham C. Goodwin (PDF in Australia)
• Synthesis of Feedback Systems (New York and London: Academic Press, 1963), by Isaac M. Horowitz (page images at HathiTrust)

• Principles of Control Systems Engineering (New York et al.: McGraw-Hill Book Co., 1960), by Vincent Del Toro and Sydney R. Parker (page images at HathiTrust)
• Analytical Design of Linear Feedback Controls (New York: J. Wiley and Sons; London: Chapman and Hall, c1957), by George C. Newton, Leonard A. Gould, and James F. Kaiser (page images at HathiTrust)

• Basic Synchros and Servomechanisms (2 volumes; New York: J. F. Rider, c1955), by Nooger & Neville Van Valkenburgh (page images at HathiTrust)
• Control System Components (New York et al.: McGraw-Hill, 1958), by John E. Gibson and Franz B. Tuteur (page images at HathiTrust)
• Cybernetics: or, Control and Communication in the Animal and the Machine (first edition; New York: J. Wiley and Sons, c1948), by Norbert Wiener (page images at HathiTrust)

• Tables of Normal Probability Functions (Washington: GPO, 1953), by Mathematical Tables Project (U.S.) (page images at HathiTrust)
• Tables of Probability Functions (2 volumes; Washington: GPO, 1941-1942), by Project for the Computation of Mathematical Tables (U.S.) and Mathematical Tables Project (U.S.) (page images at HathiTrust)
• Probability and Theory of Errors, by Robert Simpson Woodward (page images at Cornell)

• Extrapolation, Interpolation, and Smoothing of Stationary Time Series, With Engineering Applications (second printing; Cambridge, MA: Technology Press of the Massachusetts Institute of Technology; London: J. Wiley and Sons, 1950), by Norbert Wiener (page images at HathiTrust)

• Interpolation and Approximation by Rational Functions in the Complex Domain (American Mathematical Society Colloquium Publications v20, second edition; 1956), by J. L. Walsh (page images at HathiTrust)
• A Course in Interpolation and Numerical Integration for the Mathematical Laboratory, by David Gibb (page images at Cornell)
• On the Construction of Tables and on Interpolation (2 parts (Tracts for Computers #2 and 3); London: Cambridge University Press; et al., 1920), by Karl Pearson (both parts: page images at HathiTrust)
• Extrapolation, Interpolation, and Smoothing of Stationary Time Series, With Engineering Applications (second printing; Cambridge, MA: Technology Press of the Massachusetts Institute of Technology; London: J. Wiley and Sons, 1950), by Norbert Wiener (page images at HathiTrust)

• Introduction to Interval Analysis (Kongens Lyngby: Technical University of Denmark, 2002), by O. Caprani, Kaj Madsen, and Hans Bruun Nielsen (PDF with rotated pages in Denmark)

• Iterative Methods for Linear and Nonlinear Equations (Philadelphia: Society for Industrial and Applied Mathematics, 1995), by C. T. Kelley (PDF at siam.org)
• Iterative Methods for Optimization (Philadelphia: Society for Industrial and Applied Mathematics, c1999), by C. T. Kelley (PDF at siam.org)
• The Contraction Mapping Principle and Some Applications (EJDE monograph #9, 2009), by R. M. Brooks and Klaus Schmitt (PDF with commentary at ams.org)
• Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, by Richard Barrett, Michael Berry, Tony Chan, James Demmel, June Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk Van der Vorst (HTML at netlib.org)

• A Practical Manual on the Monte Carlo Method for Random Walk Problems (Los Alamos, NM: Los Alamos Scientific Laboratory of the University of California, 1957), by E. D. Cashwell and C. J. Everett, contrib. by O. W. Rechard (page images at HathiTrust)

• An Introduction to Multigrid Methods, by Pieter Wesseling (PDF files at mgnet.org)

• Alignment Charts; The Teaching of the Calculus of Probability; On the Theory of Complex Functions (Notre Dame Mathematical Lectures #4; 1944), contrib. by Lester R. Ford, A. H. Copeland, and Emil Artin (PDF files at Project Euclid)

More items available under broader and related terms at left.