Most cited papers in Numerical methods for differential equations
What are the most cited papers in Numerical methods for differential equations?
The most cited paper in Numerical methods for differential equations is "Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces" (Rainer Storn, Kenneth V. Price, 1997), with 29,587 citations. Next come "Ordinary Differential Equations" (7,320) and "Theory of Ordinary Differential Equations" (6,268).
Showing 50 of 98 papers. Every paper with more than 977 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces Rainer Storn, Kenneth V. Price · Journal of Global Optimization | Dec 1997 | 29,587 |
| 2 | Ordinary Differential Equations John M. Stewart · Cambridge University Press eBooks | 12 Oct 2017 | 7,320 |
| 3 | Theory of Ordinary Differential Equations Earl A. Coddington, Norman Levinson, Theodor Teichmann · Physics Today | Feb 1956 | 6,268 |
| 4 | State-space solutions to standard H/sub 2/ and H/sub infinity / control problems John C. Doyle, K. Glover, Pramod P. Khargonekar et al. · IEEE Transactions on Automatic Control | 1989 | 5,567 |
| 5 | P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation Berk Hess · Journal of Chemical Theory and Computation | Dec 2007 | 4,177 |
| 6 | A family of embedded Runge-Kutta formulae John R. Dormand, P.J. Prince · Journal of Computational and Applied Mathematics | Mar 1980 | 3,681 |
| 7 | Reversible multiple time scale molecular dynamics Mark E. Tuckerman, B. J. Berne, Glenn J. Martyna · The Journal of Chemical Physics | Aug 1992 | 3,655 |
| 8 | The MATLAB ODE Suite Lawrence F. Shampine, Mark W. Reichelt · SIAM Journal on Scientific Computing | 1997 | 3,654 |
| 9 | New development in freefem++ Frédéric Hecht · Journal of Numerical Mathematics | 2012 | 3,447 |
| 10 | Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn et al. · SIAM Journal on Numerical Analysis | 2002 | 3,312 |
| 11 | Analysis of Fractional Differential Equations Kai Diethelm, Neville J. Ford · Journal of Mathematical Analysis and Applications | 2002 | 3,200 |
| 12 | SUNDIALS A.C. Hindmarsh, Peter N. Brown, Keith Eric Grant et al. · ACM Transactions on Mathematical Software | Sep 2005 | 2,634 |
| 13 | On the Partial Difference Equations of Mathematical Physics Richard Courant, Kurt O. Friedrichs, Hans Lewy · IBM Journal of Research and Development | Mar 1967 | 2,475 |
| 14 | A Numerical Method for Solving Incompressible Viscous Flow Problems ALEXANDRE JOEL CHORIN · Journal of Computational Physics | Aug 1997 | 2,460 |
| 15 | Improved numerical dissipation for time integration algorithms in structural dynamics Hans M. Hilber, Thomas J.R. Hughes, Robert L. Taylor · Earthquake Engineering & Structural Dynamics | Jul 1977 | 2,436 |
| 16 | The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems Bernardo Cockburn, Chi‐Wang Shu · SIAM Journal on Numerical Analysis | 1998 | 2,432 |
| 17 | Geometric singular perturbation theory for ordinary differential equations Neil Fenichel · Journal of Differential Equations | 1979 | 2,431 |
| 18 | Mixed and Hybrid Finite Element Methods Franco Brezzi, Michel Fortin · CERN Document Server (European Organization for Nuclear Research) | 23 Nov 2011 | 2,420 |
| 19 | Artificial neural networks for solving ordinary and partial differential equations I.E. Lagaris, A. Likas, D.I. Fotiadis · IEEE Transactions on Neural Networks | 1998 | 2,402 |
| 20 | Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later C Moler, Charles Van Loan · SIAM Review | 2003 | 2,399 |
| 21 | A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method Jaeung Chung, Gregory M. Hulbert · Journal of Applied Mechanics | Jun 1993 | 2,350 |
| 22 | Numerical solution of saddle point problems Michele Benzi, Gene Howard Golub, Jörg Liesen · Acta Numerica | 19 Apr 2005 | 2,339 |
| 23 | Construction of higher order symplectic integrators Haruo Yoshida · Physics Letters A | Nov 1990 | 2,327 |
| 24 | DIFFERENTIAL-DIFFERENCE EQUATIONS Kenneth L. Cooke · WORLD SCIENTIFIC eBooks | Feb 1987 | 2,304 |
| 25 | Analysis of Numerical Methods Eugene Isaacson, Herbert B. Keller, George H. Weiss · Physics Today | Jul 1967 | 2,289 |
| 26 | Structure of Phenomenological Lagrangians. I Sidney Coleman, Jane A. Wess, Bruno Zumino · Physical Review | 25 Jan 1969 | 2,191 |
| 27 | The Painlevé property for partial differential equations John E. Weiss, M. Tabor, G. F. Carnevale · Journal of Mathematical Physics | Mar 1983 | 2,164 |
| 28 | Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model Akio Arakawa, V. R. Lamb · Methods in computational physics | 1977 | 2,158 |
| 29 | Lectures on Cauchy's Problem in Linear Partial Differential Equations Jacques Hadamard, Philip Μ. Morse · Physics Today | Aug 1953 | 2,109 |
| 30 | A Technique for the Numerical Solution of Certain Integral Equations of the First Kind David Lee Phillips · Journal of the ACM | 1962 | 2,042 |
| 31 | Nonlinear Systems Analysis M. Vidyasagar, C. Desoer · IEEE Transactions on Systems Man and Cybernetics | Aug 1980 | 2,033 |
| 32 | A cone complementarity linearization algorithm for static output-feedback and related problems Laurent El Ghaoui, François Oustry, M. Ait-Rami · IEEE Transactions on Automatic Control | 1997 | 2,028 |
| 33 | A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) Ronald P. Fedkiw, Tariq D. Aslam, Barry Merriman et al. · Journal of Computational Physics | Jul 1999 | 2,011 |
| 34 | The FEniCS Project Version 1.5 Martin Sandve Alnæs, Jan Blechta, Johan E. Hake et al. · Department of Earth Sciences EPrints Repository | 2015 | 1,987 |
| 35 | Jacobian-free Newton–Krylov methods: a survey of approaches and applications Dana A. Knoll, David Elliot Keyes · Journal of Computational Physics | 9 Oct 2003 | 1,956 |
| 36 | TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework Bernardo Cockburn, Chi‐Wang Shu · Mathematics of Computation | 1989 | 1,945 |
| 37 | The partial differential equation u t + uu x = μ xx Eberhard Hopf · Communications on Pure and Applied Mathematics | Sep 1950 | 1,918 |
| 38 | Dummy Endogenous Variables in a Simultaneous Equation System James J. Heckman · Econometrica | Jul 1978 | 1,906 |
| 39 | Some global results for nonlinear eigenvalue problems Paul H. Rabinowitz · Journal of Functional Analysis | Jun 1971 | 1,896 |
| 40 | Domain decomposition: Parallel multilevel methods for elliptic partial differential equations By Barry Smith · Computers & Mathematics with Applications | Feb 1997 | 1,870 |
| 41 | A hybrid symplectic integrator that permits close encounters between massive bodies John Chambers · Monthly Notices of the Royal Astronomical Society | 16 Apr 1999 | 1,864 |
| 42 | Perturbation Methods in Applied Mathematics Julian D. Cole, Lawrence Elliott Levine · IEEE Transactions on Systems Man and Cybernetics | Nov 1973 | 1,842 |
| 43 | Explicit reversible integrators for extended systems dynamics Glenn J. Martyna, Mark E. Tuckerman, Douglas J. Tobias et al. · Molecular Physics | 10 Apr 1996 | 1,823 |
| 44 | Continuous finite-time stabilization of the translational and rotational double integrators Sanjay P. Bhat, Dennis S. Bernstein · IEEE Transactions on Automatic Control | May 1998 | 1,705 |
| 45 | Data-driven discovery of partial differential equations Samuel Rudy, Steven L. Brunton, Joshua L. Proctor et al. · Science Advances | 7 Apr 2017 | 1,597 |
| 46 | Discrete mechanics and variational integrators Jerrold Eldon Marsden, Matthew West · Acta Numerica | May 2001 | 1,593 |
| 47 | On the Stability of the linear Transformation in Banach Spaces. Tosio Aoki · Journal of the Mathematical Society of Japan | Sep 1950 | 1,560 |
| 48 | TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems Bernardo Cockburn, San‐Yih Lin, Chi‐Wang Shu · Journal of Computational Physics | Sep 1989 | 1,531 |
| 49 | MATCONT Annick Dhooge, Willy J. F. Govaerts, Yuri A. Kuznetsov · ACM Transactions on Mathematical Software | Jun 2003 | 1,490 |
| 50 | An accurate and efficient scheme for propagating the time dependent Schrödinger equation Hillel Tal‐Ezer, Ronnie Kosloff · The Journal of Chemical Physics | Nov 1984 | 1,478 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.