EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues RAIRO. Anal. numér., 12 3 (1978) 237-245 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

A Boot-Strapping Technique to Design Unconditionally Positive Dense Output Formulae for Modified Patankar-Runge-Kutta Methods

Thomas Izgin
Communications on Applied Mathematics and Computation (2025)
https://doi.org/10.1007/s42967-025-00480-8

PositiveIntegrators.jl: A Julia library of positivity-preserving time integration methods

Stefan Kopecz, Joshua Lampert and Hendrik Ranocha
Journal of Open Source Software 10 (109) 8130 (2025)
https://doi.org/10.21105/joss.08130

On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters

Thomas Izgin, Stefan Kopecz, Andreas Meister and Amandine Schilling
Numerical Algorithms 96 (3) 1221 (2024)
https://doi.org/10.1007/s11075-024-01770-7

Numerical threshold stability of a nonlinear age-structured reaction diffusion heroin transmission model

X. Liu, M. Zhang and Z.W. Yang
Applied Numerical Mathematics 204 291 (2024)
https://doi.org/10.1016/j.apnum.2024.06.016

Framework for solving dynamics of Ca2+ ion concentrations in liver cells numerically: Analysis of a non‐negativity‐preserving non‐standard finite‐difference method

Benjamin Wacker
Mathematical Methods in the Applied Sciences 46 (16) 16625 (2023)
https://doi.org/10.1002/mma.9464

Error estimates for fully discrete BDF finite element approximations of the Allen–Cahn equation

Georgios Akrivis and Buyang Li
IMA Journal of Numerical Analysis 42 (1) 363 (2022)
https://doi.org/10.1093/imanum/draa065

On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes

Thomas Izgin, Stefan Kopecz and Andreas Meister
SIAM Journal on Numerical Analysis 60 (6) 3029 (2022)
https://doi.org/10.1137/22M1480318

Maximum Principle Preserving Space and Time Flux Limiting for Diagonally Implicit Runge–Kutta Discretizations of Scalar Convection-diffusion Equations

Manuel Quezada de Luna and David I. Ketcheson
Journal of Scientific Computing 92 (3) (2022)
https://doi.org/10.1007/s10915-022-01922-8

Positivity-preserving adaptive Runge–Kutta methods

Stephan Nüßlein, Hendrik Ranocha and David I. Ketcheson
Communications in Applied Mathematics and Computational Science 16 (2) 155 (2021)
https://doi.org/10.2140/camcos.2021.16.155

Computation of Optimal Linear Strong Stability Preserving Methods Via Adaptive Spectral Transformations of Poisson–Charlier Measures

Rachid Ait-Haddou
Journal of Scientific Computing 88 (3) (2021)
https://doi.org/10.1007/s10915-021-01582-0

Kernel density estimation with linked boundary conditions

Matthew J. Colbrook, Zdravko I. Botev, Karsten Kuritz and Shev MacNamara
Studies in Applied Mathematics 145 (3) 357 (2020)
https://doi.org/10.1111/sapm.12322

Invariance Preserving Discretization Methods of Dynamical Systems

Zoltán Horváth, Yunfei Song and Tamás Terlaky
Vietnam Journal of Mathematics 46 (4) 803 (2018)
https://doi.org/10.1007/s10013-018-0305-z

Technical Note: A generic law-of-the-minimum flux limiter for simulating substrate limitation in biogeochemical models

J. Y. Tang and W. J. Riley
Biogeosciences 13 (3) 723 (2016)
https://doi.org/10.5194/bg-13-723-2016

Positive Second Order Finite Difference Methods on Fokker-Planck Equations with Dirac Initial Data

Fabien Le Floc'h
SSRN Electronic Journal (2015)
https://doi.org/10.2139/ssrn.2600500

Positive Second Order Finite Difference Methods on Fokker-Planck Equations with Dirac Initial Data - Application in Finance

Fabien Le Floc'h
SSRN Electronic Journal (2015)
https://doi.org/10.2139/ssrn.2605160

Rosenbrock-type methods with Inexact AMF for the time integration of advection–diffusion–reaction PDEs

S. González-Pinto, D. Hernández-Abreu and S. Pérez-Rodríguez
Journal of Computational and Applied Mathematics 262 304 (2014)
https://doi.org/10.1016/j.cam.2013.10.050

Positivity preserving discretization of time dependent semiconductor drift–diffusion equations

Markus Brunk and Anne Kværnø
Applied Numerical Mathematics 62 (10) 1289 (2012)
https://doi.org/10.1016/j.apnum.2012.06.016

Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods

W. Hundsdorfer, A. Mozartova and M. N. Spijker
Journal of Scientific Computing 50 (2) 265 (2012)
https://doi.org/10.1007/s10915-011-9487-1

A second-order positivity preserving scheme for semilinear parabolic problems

Eskil Hansen, Felix Kramer and Alexander Ostermann
Applied Numerical Mathematics 62 (10) 1428 (2012)
https://doi.org/10.1016/j.apnum.2012.06.003

Positivity and Conservation Properties of Some Integration Schemes for Mass Action Kinetics

L. Formaggia and A. Scotti
SIAM Journal on Numerical Analysis 49 (3) 1267 (2011)
https://doi.org/10.1137/100789592

On a stochastic reaction–diffusion system modeling pattern formation on seashells

Jan Kelkel and Christina Surulescu
Journal of Mathematical Biology 60 (6) 765 (2010)
https://doi.org/10.1007/s00285-009-0284-5

Combination of nonstandard schemes and Richardson’s extrapolation to improve the numerical solution of population models

Gilberto González-Parra, Abraham J. Arenas and Benito M. Chen-Charpentier
Mathematical and Computer Modelling 52 (7-8) 1030 (2010)
https://doi.org/10.1016/j.mcm.2010.03.015

Advanced Computational Methods in Science and Engineering

S. van Veldhuizen, C. Vuik and C. R. Kleijn
Lecture Notes in Computational Science and Engineering, Advanced Computational Methods in Science and Engineering 71 47 (2009)
https://doi.org/10.1007/978-3-642-03344-5_3

Comparison of ODE methods for laminar reacting gas flow simulations

S. van Veldhuizen, C. Vuik and C.R. Kleijn
Numerical Methods for Partial Differential Equations 24 (3) 1037 (2008)
https://doi.org/10.1002/num.20305

A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems

Jorn Bruggeman, Hans Burchard, Bob W. Kooi and Ben Sommeijer
Applied Numerical Mathematics 57 (1) 36 (2007)
https://doi.org/10.1016/j.apnum.2005.12.001

Runge–Kutta convolution quadrature methods for well-posed equations with memory

M. P. Calvo, E. Cuesta and C. Palencia
Numerische Mathematik 107 (4) 589 (2007)
https://doi.org/10.1007/s00211-007-0107-9

BACKWARD EULER METHOD AS A POSITIVITY PRESERVING METHOD FOR ABSTRACT INTEGRAL EQUATIONS OF CONVOLUTION TYPE

E. Cuesta, M.P. Calvo and C. Palencia
IFAC Proceedings Volumes 39 (11) 517 (2006)
https://doi.org/10.3182/20060719-3-PT-4902.00086

On positivity, shape, and norm-bound preservation of time-stepping methods for semigroups

Mihály Kovács
Journal of Mathematical Analysis and Applications 304 (1) 115 (2005)
https://doi.org/10.1016/j.jmaa.2004.09.069

Numerical simulation of a point-source initiated flame ball with heat losses

Jacques Audounet, Jean-Michel Roquejoffre and Hélène Rouzaud
ESAIM: Mathematical Modelling and Numerical Analysis 36 (2) 273 (2002)
https://doi.org/10.1051/m2an:2002017

Convergence and nonnegativity of numerical methods for an integrodifferential equation describing batch grinding

G. Stoyan, C. Mihálykó and Z. Ulbert
Computers & Mathematics with Applications 35 (12) 69 (1998)
https://doi.org/10.1016/S0898-1221(98)00097-2

Numerical analysis of three‐time‐level finite difference schemes for unsteady diffusion–convection problems

Alain Rigal
International Journal for Numerical Methods in Engineering 30 (2) 307 (1990)
https://doi.org/10.1002/nme.1620300207

Stability radius of polynomials occurring in the numerical solution of initial value problems

Roeland P. van der Marel
BIT Numerical Mathematics 30 (3) 516 (1990)
https://doi.org/10.1007/BF01931665

Numerical analysis of two‐level finite difference schemes for unsteady diffusion–convection problems

Alain Rigal
International Journal for Numerical Methods in Engineering 28 (5) 1001 (1989)
https://doi.org/10.1002/nme.1620280503

Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations

J.F.B.M. Kraaijevanger, H.W.J. Lenferink and M.N. Spijker
Journal of Computational and Applied Mathematics 20 67 (1987)
https://doi.org/10.1016/0377-0427(87)90126-9

Absolute monotonicity of rational functions occurring in the numerical solution of initial value problems

J. A. van de Griend and J. F. B. M. Kraaijevanger
Numerische Mathematik 49 (4) 413 (1986)
https://doi.org/10.1007/BF01389539

Absolute monotonicity of polynomials occurring in the numerical solution of initial value problems

J. F. B. M. Kraaijevanger
Numerische Mathematik 48 (3) 303 (1986)
https://doi.org/10.1007/BF01389477

Order Stars, Approximations and Finite Differences. III Finite Differences for $u_t = \omega u_{xx} $

A. Iserles
SIAM Journal on Mathematical Analysis 16 (5) 1020 (1985)
https://doi.org/10.1137/0516076

Invariant Regions and asymptotic behaviour for the numerical solution of reaction-diffusion systems by a class of alternating direction methods

C. Mastroserio and M. Montrone
Calcolo 21 (3) 269 (1984)
https://doi.org/10.1007/BF02576537

Instability in Runge-Kutta schemes for simulation of oil recovery

P. H. Sammon and P. Forsyth
BIT Numerical Mathematics 24 (3) 373 (1984)
https://doi.org/10.1007/BF02136036