Most cited papers in Differential Equations and Numerical Methods
What are the most cited papers in Differential Equations and Numerical Methods?
The most cited paper in Differential Equations and Numerical Methods is "Deterministic Nonperiodic Flow" (Edward N. Lorenz, 1963), with 19,616 citations. Next come "Perturbation Methods" (4,699) and "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators" (4,448).
Showing 50 of 99 papers. Every paper with more than 562 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Deterministic Nonperiodic Flow Edward N. Lorenz · Journal of the Atmospheric Sciences | Mar 1963 | 19,616 |
| 2 | Perturbation Methods A. H. Nayfeh, Vimal Singh · IEEE Transactions on Systems Man and Cybernetics | May 1978 | 4,699 |
| 3 | An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Cornelius Lanczos · Journal of research of the National Bureau of Standards | Oct 1950 | 4,448 |
| 4 | An integrable shallow water equation with peaked solitons Roberto Camassa, Darryl D. Holm · Physical Review Letters | 13 Sep 1993 | 3,754 |
| 5 | Difference Methods for Initial-Value Problems Robert D. Richtmyer, E. H. Dill · Physics Today | Apr 1959 | 3,233 |
| 6 | Analysis of Fractional Differential Equations Kai Diethelm, Neville J. Ford · Journal of Mathematical Analysis and Applications | 2002 | 3,200 |
| 7 | Variational iteration method – a kind of non-linear analytical technique: some examples Ji‐Huan He · International Journal of Non-Linear Mechanics | Jul 1999 | 2,553 |
| 8 | 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 |
| 9 | Geometric singular perturbation theory for ordinary differential equations Neil Fenichel · Journal of Differential Equations | 1979 | 2,431 |
| 10 | Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow Byron C. Sakiadis · AIChE Journal | Mar 1961 | 2,362 |
| 11 | Analysis of Numerical Methods Eugene Isaacson, Herbert B. Keller, George H. Weiss · Physics Today | Jul 1967 | 2,289 |
| 12 | SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS Ji‐Huan He · International Journal of Modern Physics B | 19 Apr 2006 | 2,215 |
| 13 | Nonlinear Systems Analysis M. Vidyasagar, C. Desoer · IEEE Transactions on Systems Man and Cybernetics | Aug 1980 | 2,033 |
| 14 | New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection–Diffusion Equations Alexander Kurganov, Eitan Tadmor · Journal of Computational Physics | May 2000 | 1,964 |
| 15 | Weak solutions of nonlinear hyperbolic equations and their numerical computation Peter D. Lax · Communications on Pure and Applied Mathematics | Feb 1954 | 1,851 |
| 16 | Finite difference/spectral approximations for the time-fractional diffusion equation Yumin Lin, Chuanju Xu · Journal of Computational Physics | 15 Feb 2007 | 1,843 |
| 17 | Perturbation Methods in Applied Mathematics Julian D. Cole, Lawrence Elliott Levine · IEEE Transactions on Systems Man and Cybernetics | Nov 1973 | 1,842 |
| 18 | Existence of solitary waves in higher dimensions Walter A. Strauss · Communications in Mathematical Physics | Jun 1977 | 1,834 |
| 19 | On the homotopy analysis method for nonlinear problems Shijun Liao · Applied Mathematics and Computation | 11 Oct 2003 | 1,787 |
| 20 | On a quasi-linear parabolic equation occurring in aerodynamics Julian D. Cole · Quarterly of Applied Mathematics | Oct 1951 | 1,765 |
| 21 | The finite element method with Lagrangian multipliers Ivo M. Babuska · Numerische Mathematik | Jun 1973 | 1,641 |
| 22 | Wave breaking for nonlinear nonlocal shallow water equations Adrian Constantin, Joachim Escher · Acta Mathematica | 1998 | 1,499 |
| 23 | Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind Johannes M. Nitsche · Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg | Jul 1971 | 1,476 |
| 24 | Finite-Difference Methods for Partial Differential Equations George E. Forsythe, Wolfgang R. Wasow, William Nachbar · Physics Today | Apr 1961 | 1,352 |
| 25 | Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields John M. Guckenheimer, Philip J. Holmes, Marshall Slemrod · Journal of Applied Mechanics | Dec 1984 | 1,291 |
| 26 | Progress in Nonlinear Differential Equations and their Applications Amandine Aftalion · HAL (Le Centre pour la Communication Scientifique Directe) | 2006 | 1,261 |
| 27 | A fully discrete difference scheme for a diffusion-wave system Zhi‐zhong Sun, Xiaonan Wu · Applied Numerical Mathematics | 30 Apr 2005 | 1,249 |
| 28 | The Theory of Difference Schemes ALEXANDER A. SAMARSKII, VD Radulescu, · Applied Mechanics Reviews | 29 Mar 2001 | 1,220 |
| 29 | Geometric singular perturbation theory Christopher K. R. T. Jones · Lecture notes in mathematics | 1995 | 1,154 |
| 30 | Positive solutions for boundary value problem of nonlinear fractional differential equation Zhanbing Bai, Haishen Lü · Journal of Mathematical Analysis and Applications | 11 Apr 2005 | 1,102 |
| 31 | A novel finite difference formulation for differential expressions involving both first and second derivatives D. BRIAN SPALDING · International Journal for Numerical Methods in Engineering | Jul 1972 | 1,101 |
| 32 | Exponential integrators Marlis Hochbruck, Alexander Ostermann · Acta Numerica | May 2010 | 1,073 |
| 33 | Quasilinear elliptic-parabolic differential equations Hans Wilhelm Alt, Stephan Luckhaus · Mathematische Zeitschrift | Sep 1983 | 1,055 |
| 34 | Convergence of approximation schemes for fully nonlinear second order equations Guy Barles, Panagiotis E. Souganidis · Asymptotic Analysis | May 1991 | 1,052 |
| 35 | Perturbation Methods in Applied Mathematics Harold Weitzner, Julian D. Cole · Mathematics of Computation | Jul 1969 | 1,040 |
| 36 | Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation Martin Stynes, Eugene O’Riordan, J.L. Gracia · SIAM Journal on Numerical Analysis | 2017 | 1,027 |
| 37 | Numerical Methods for Ordinary Differential Systems: The Initial Value Problem John D. Lambert | Sep 1991 | 1,022 |
| 38 | Asymptotic methods in the theory of non-linear oscillations N. DeClaris · Proceedings of the IEEE | 1963 | 1,009 |
| 39 | On some non-linear elliptic differential-functional equations Philip E. Hartman, Guido Stampacchia · Acta Mathematica | 1966 | 1,005 |
| 40 | Fourth-Order Time-Stepping for Stiff PDEs Aly-Khan Kassam, Lloyd N. Trefethen · SIAM Journal on Scientific Computing | 2005 | 970 |
| 41 | On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature Sean A. Twomey · Journal of the ACM | 1963 | 964 |
| 42 | Finite difference approximations for two-sided space-fractional partial differential equations Mark M. Meerschaert, Charles Tadjeran · Applied Numerical Mathematics | 18 Mar 2005 | 952 |
| 43 | Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria Steven P. Hirshman, J. C. Whitson · The Physics of Fluids | Dec 1983 | 919 |
| 44 | A new difference scheme for the time fractional diffusion equation Anatoly A. Alikhanov · Journal of Computational Physics | 4 Oct 2014 | 898 |
| 45 | A MATLAB differentiation matrix suite J. A. C. Weideman, S C Reddy · ACM Transactions on Mathematical Software | Dec 2000 | 894 |
| 46 | A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS Henry P. McKean · Proceedings of the National Academy of Sciences | Dec 1966 | 888 |
| 47 | Stochastic differential equations with reflecting boundary conditions Pierre‐Louis Lions, Alain‐Sol Sznitman · Communications on Pure and Applied Mathematics | Jul 1984 | 865 |
| 48 | Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988 Rolland L. Hardy · Computers & Mathematics with Applications | 1990 | 862 |
| 49 | The homotopy perturbation method for nonlinear oscillators with discontinuities Ji‐Huan He · Applied Mathematics and Computation | 7 Jul 2003 | 854 |
| 50 | Added-mass effect in the design of partitioned algorithms for fluid–structure problems Paola Causin, J.-F. Gerbeau, Fabio Nobile · Computer Methods in Applied Mechanics and Engineering | 25 Jan 2005 | 850 |
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.