Most-cited papers on Numerical Methods and Convergence

Ranked by citation count via OpenAlex. Citations update on a rolling basis; list regenerates every 24h.

1. Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

   1998 · SIAM Journal on Optimization · Alizadeh, Farid, Haeberly, Jean-Pierre A., Overton, Michael L.

   494 cited

2. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

   2012 · The Annals of Applied Probability · Hutzenthaler, Martin, Jentzen, Arnulf, Kloeden, Peter E.

   437 cited

3. Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results

   2009 · Mathematical Programming · Cartis, Coralia, Gould, Nicholas I. M., Toint, Philippe L.

   343 cited

4. Projection Method I: Convergence and Numerical Boundary Layers

   1995 · SIAM Journal on Numerical Analysis · Weinan, E, Liu, Jian‐Guo

   226 cited

5. Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients

   2012 · Journal of Computational and Applied Mathematics · Mao, Xuerong, Szpruch, Łukasz

   167 cited

6. Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations

   2004 · SIAM Journal on Numerical Analysis · Pelinovsky, Dmitry E., Stepanyants, Yury

   166 cited

7. Analytical and Numerical Studies of the Relative Convergence Phenomenon Arising in the Solution of an Integral Equation by the Moment Method

   1972 · IEEE Transactions on Microwave Theory and Techniques · Mittra, R., Itoh, T., Li, Ti-Shu

   162 cited

8. Numerical methods for non-LTE line radiative transfer: Performance and convergence characteristics

   2002 · Astronomy and Astrophysics · Zadelhoff, Gerd‐Jan van, Dullemond, C. P., Tak, F. van der et al.

   140 cited

9. THE NATURE OF THE WARM/HOT INTERGALACTIC MEDIUM. I. NUMERICAL METHODS, CONVERGENCE, AND O VI ABSORPTION

   2011 · The Astrophysical Journal · Smith, Britton, Hallman, Eric, Shull, J. Michael et al.

   123 cited

10. A high accuracy numerical method and its convergence for time-fractional Black-Scholes equation governing European options

    2019 · Applied Numerical Mathematics · Roul, Pradip

    116 cited

11. On the convergence of the multi‐point flux approximation O‐method: Numerical experiments for discontinuous permeability

    2005 · Numerical Methods for Partial Differential Equations · Eigestad, G. T., Klausen, Runhild A.

    107 cited

12. Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability

    2018 · IMA Journal of Numerical Analysis · Li, Xiaoyue, Mao, Xuerong, Yin, George

    98 cited

13. An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis

    2010 · Computers & Mathematics with Applications · Ghoreishi, F., Yazdani, S.

    96 cited

14. Numerical investigation on convergence of boundary knot method in the analysis of homogeneous Helmholtz, modified Helmholtz, and convection–diffusion problems

    2003 · Computer Methods in Applied Mechanics and Engineering · Chen, W., Hon, Y.C.

    94 cited

15. The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method

    1999 · SIAM Journal on Numerical Analysis · Golse, François, Jin, Shi, Levermore, C. David

    90 cited

16. Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

    2009 · IMA Journal of Applied Mathematics · Zhuang, Peixian, Liu, F., Anh, Vo et al.

    81 cited

17. Convergence of numerical methods for valuing path-dependent options using interpolation

    2002 · Review of Derivatives Research · Forsyth, Peter, Vetzal, K.R., Zvan, R.

    78 cited

18. Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh-Ritz method

    1999 · International Journal for Numerical Methods in Engineering · Smith, Scott T., Bradford, Mark A., Oehlers, Deric J.

    75 cited

19. A numerical method for a converging cylindrical shock

    1957 · Journal of Fluid Mechanics · Payne, R. B.

    73 cited

20. Convergence and Accuracy of Numerical Methods for Trajectory Calculations

    1993 · Journal of Applied Meteorology · Seibert, Petra

    70 cited

21. Mixed finite element methods for unilateral problems: convergence analysis and numerical studies

    2001 · Mathematics of Computation · Coorevits, Patrice, Hild, Patrick, Lhalouani, Khalid et al.

    69 cited

22. A numerical procedure for the fictitious support pressure in the application of the convergence–confinement method for circular tunnel design

    2015 · International Journal of Rock Mechanics and Mining Sciences · Cui, Lan, Zheng, Junjie, Zhang, Rongjun et al.

    67 cited

23. A numerical solution of the Klein–Gordon equation and convergence of the decomposition method

    2003 · Applied Mathematics and Computation · Kaya, Doǧan, El‐Sayed, Salah M.

    66 cited

24. Convergence Analysis of the Solution of Retarded and Neutral Delay Differential Equations by Continuous Numerical Methods

    1998 · SIAM Journal on Numerical Analysis · Enright, W. H., Hayashi, Hiroshi

    63 cited

25. Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton–Krylov method

    2009 · Journal of Computational Physics · Lemieux, Jean‐François, Tremblay, Bruno, Sedláčék, Jan et al.

    62 cited

26. A new numerical method to solve pantograph delay differential equations with convergence analysis

    2021 · Advances in Difference Equations · Jafari, Hossein, Mahmoudi, M., Skandari, M. H. Noori

    54 cited

27. On the Rate of Convergence of the Bergman–Vekua Method for the Numerical Solution of Elliptic Boundary Value Problems

    1974 · SIAM Journal on Numerical Analysis · Eisenstat, Stanley C.

    50 cited

28. Uniform-in-time convergence of numerical methods for non-linear degenerate parabolic equations

    2015 · Numerische Mathematik · Droniou, Jérôme, Eymard, Robert

    46 cited

29. Numerical simulation of the convergence of a bolt‐supported tunnel through a homogenization method

    1995 · International Journal for Numerical and Analytical Methods in Geomechanics · Bernaud, Denise, Buhan, Patrick de, Maghous, Samir

    44 cited

30. Local Convergence of an Inexact-Restoration Method and Numerical Experiments

    2005 · Journal of Optimization Theory and Applications · Birgin, Ernesto G., Martı́nez, J. M.

    44 cited