Keyword

multistep methods

Description: Numerical methods for solving differential equations that use values from multiple steps to approximate a solution.

Primary topic: Numerical methods for differential equations (69%)

OpenAlex ID: keywords/multistep-methods

Iterative Solution of Nonlinear Equations in Several Variables

2000 · J. M. Ortega, W. C. Rheinboldt · Society for Industrial and Applied Mathematics eBooks · 6,859

Solving ordinary differential equations I. nonstiff problems

1987 · Hairer, Ernst, Norsett, Syvert Paul, et al. · Mathematics and Computers in Simulation · 4,077

Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

1995 · K. E. Brenan, S. L. Campbell, et al. · Society for Industrial and Applied Mathematics eBooks · 3,411

Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations

2009 · Ernst Hairer, Christian Lubich, et al. · 3,126

Some methods of speeding up the convergence of iteration methods

1964 · B.T. Polyak · USSR Computational Mathematics and Mathematical Physics · 2,867

Solving Ordinary Differential Equations I

1987 · Ernst Hairer, Syvert Paul Nørsett, et al. · Springer series in computational mathematics · 2,398

VODE: A Variable-Coefficient ODE Solver

1989 · Peter N. Brown, George D. Byrne, et al. · SIAM Journal on Scientific and Statistical Computing · 1,640

Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

1993 · Ernst Hairer, Syvert P. Nørsett, et al. · 1,174

Gradient methods for minimizing composite objective function

2007 · Yu. Nesterov · 867

Some general implicit processes for the numerical solution of differential equations

1963 · H. H. Rosenbrock · The Computer Journal · 571

Ordinary Differential Equations

1983 · James S. Vandergraft · Elsevier eBooks · 476

A First Course in the Numerical Analysis of Differential Equations

2008 · Arieh Iserles · Cambridge University Press eBooks · 461

Numerical integration of ordinary differential equations on manifolds

1993 · P. E. Crouch, R. Grossman · Journal of Nonlinear Science · 333

Solving differential problems by multistep initial and boundary value methods

1998 · Luigi Brugnano, Donato Trigiante · 317

Data driven governing equations approximation using deep neural networks

2019 · Tong Qin, Kailiang Wu, et al. · Journal of Computational Physics · 284

On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations

2005 · Sigal Gottlieb · Journal of Scientific Computing · 284

Recent Progress in Extrapolation Methods for Ordinary Differential Equations

1985 · P. Deuflhard · SIAM Review · 268

Order stars and stability theorems

1978 · G. Wanner, E. Hairer, et al. · BIT Numerical Mathematics · 241

General Linear Methods for Ordinary Differential Equations

2009 · Zdzisław Jackiewicz · Wiley eBooks · 236

Generalized integrating factor methods for stiff PDEs

2004 · S. Krogstad · Journal of Computational Physics · 233

A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations

1965 · J. C. Butcher · Journal of the ACM · 233

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Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing

2010 · Simon Setzer · International Journal of Computer Vision · 221

The Numerical Integration of Ordinary Differential Equations

1967 · C. W. Gear · Mathematics of Computation · 215

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Numerical Solution of Ordinary Differential Equations

2009 · Kendall E. Atkinson, Weimin Han, et al. · Wiley eBooks · 210

Numerical methods for ordinary differential equations: initial value problems

2011 · Choice Reviews Online · 209

Works count: 1,731

Citation count: 44,930