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:

This article has been cited by the following article(s):

Framework for solving dynamics of Ca2+$$ {\mathrm{Ca}}^{2+} $$ 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 (2023)
DOI: 10.1002/mma.9464
See this article

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)
DOI: 10.1137/22M1480318
See this article

Issues with positivity-preserving Patankar-type schemes

Davide Torlo, Philipp Öffner and Hendrik Ranocha
Applied Numerical Mathematics 182 117 (2022)
DOI: 10.1016/j.apnum.2022.07.014
See this article

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)
DOI: 10.1093/imanum/draa065
See this article

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)
DOI: 10.1007/s10915-022-01922-8
See this article

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)
DOI: 10.1007/s10915-021-01582-0
See this article

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)
DOI: 10.2140/camcos.2021.16.155
See this article

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)
DOI: 10.1111/sapm.12322
See this article

A comprehensive theory on generalized BBKS schemes

Andrés I. Ávila, Stefan Kopecz and Andreas Meister
Applied Numerical Mathematics 157 19 (2020)
DOI: 10.1016/j.apnum.2020.05.027
See this article

Applications of Magnus expansions and pseudospectra to Markov processes

A. ISERLES and S. MACNAMARA
European Journal of Applied Mathematics 30 (2) 400 (2019)
DOI: 10.1017/S0956792518000177
See this article

2017 MATRIX Annals

Colin Fox, Richard A. Norton, Malcolm E. K. Morrison and Timothy C. A. Molteno
MATRIX Book Series, 2017 MATRIX Annals 2 13 (2019)
DOI: 10.1007/978-3-030-04161-8_2
See this article

Positivity for Convective Semi-discretizations

Imre Fekete, David I. Ketcheson and Lajos Lóczi
Journal of Scientific Computing 74 (1) 244 (2018)
DOI: 10.1007/s10915-017-0432-9
See this article

Invariance Preserving Discretization Methods of Dynamical Systems

Zoltán Horváth, Yunfei Song and Tamás Terlaky
Vietnam Journal of Mathematics 46 (4) 803 (2018)
DOI: 10.1007/s10013-018-0305-z
See this article

Structure-preserving discretization of the chemical master equation

Ludwig Gauckler and Harry Yserentant
BIT Numerical Mathematics 57 (3) 753 (2017)
DOI: 10.1007/s10543-017-0651-3
See this article

Herman Deconinck and Mario Ricchiuto
1 (2017)
DOI: 10.1002/9781119176817.ecm2054
See this article

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)
DOI: 10.5194/bg-13-723-2016
See this article

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)
DOI: 10.2139/ssrn.2605160
See this article

J. Y. Tang and W. J. Riley
(2015)
DOI: 10.5194/bgd-12-13399-2015
See this article

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

Fabien Le Floc'h
SSRN Electronic Journal (2015)
DOI: 10.2139/ssrn.2600500
See this article

Rational functions with maximal radius of absolute monotonicity

Lajos Lóczi and David I. Ketcheson
LMS Journal of Computation and Mathematics 17 (1) 159 (2014)
DOI: 10.1112/S1461157013000326
See this article

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)
DOI: 10.1016/j.cam.2013.10.050
See this article

A second-order positivity preserving scheme for semilinear parabolic problems

Eskil Hansen, Felix Kramer and Alexander Ostermann
Applied Numerical Mathematics 62 (10) 1428 (2012)
DOI: 10.1016/j.apnum.2012.06.003
See this article

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)
DOI: 10.1007/s10915-011-9487-1
See this article

Positivity preserving discretization of time dependent semiconductor drift–diffusion equations

Markus Brunk and Anne Kværnø
Applied Numerical Mathematics 62 (10) 1289 (2012)
DOI: 10.1016/j.apnum.2012.06.016
See this article

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)
DOI: 10.1137/100789592
See this article

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

Jan Kelkel and Christina Surulescu
Journal of Mathematical Biology 60 (6) 765 (2010)
DOI: 10.1007/s00285-009-0284-5
See this article

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)
DOI: 10.1016/j.mcm.2010.03.015
See this article

Positivity inheritance for linear problems

A.K. Baum and Volker Mehrmann
PAMM 10 (1) 597 (2010)
DOI: 10.1002/pamm.201010291
See this article

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)
DOI: 10.1007/978-3-642-03344-5_3
See this article

Stabilized residual distribution for shallow water simulations

Mario Ricchiuto and Andreas Bollermann
Journal of Computational Physics 228 (4) 1071 (2009)
DOI: 10.1016/j.jcp.2008.10.020
See this article

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)
DOI: 10.1002/num.20305
See this article

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)
DOI: 10.1007/s00211-007-0107-9
See this article

Positivity of exponential Runge–Kutta methods

Alexander Ostermann and Marnix van Daele
BIT Numerical Mathematics 47 (2) 419 (2007)
DOI: 10.1007/s10543-007-0124-1
See this article

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)
DOI: 10.1016/j.apnum.2005.12.001
See this article

Numerical Mathematics and Advanced Applications

Alexander Ostermann and Mechthild Thalhammer
Numerical Mathematics and Advanced Applications 564 (2006)
DOI: 10.1007/978-3-540-34288-5_53
See this article

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)
DOI: 10.3182/20060719-3-PT-4902.00086
See this article

On the positivity step size threshold of Runge–Kutta methods

Zoltán Horváth
Applied Numerical Mathematics 53 (2-4) 341 (2005)
DOI: 10.1016/j.apnum.2004.08.026
See this article

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)
DOI: 10.1016/j.jmaa.2004.09.069
See this article

On the positivity of matrix-vector products

Zoltán Horváth
Linear Algebra and its Applications 393 253 (2004)
DOI: 10.1016/j.laa.2004.03.012
See this article

Herman Deconinck and Mario Ricchiuto
(2004)
DOI: 10.1002/0470091355.ecm054
See this article

The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods

A Gerisch and R Weiner
Computers & Mathematics with Applications 45 (1-3) 53 (2003)
DOI: 10.1016/S0898-1221(03)80007-X
See this article

Implicit–explicit time stepping with spatial discontinuous finite elements

Willem Hundsdorfer and Jérôme Jaffré
Applied Numerical Mathematics 45 (2-3) 231 (2003)
DOI: 10.1016/S0168-9274(02)00192-7
See this article

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)
DOI: 10.1051/m2an:2002017
See this article

A positive splitting method for mixed hyperbolic-parabolic systems

Alf Gerisch, David F. Griffiths, R�diger Weiner and Mark A. J. Chaplain
Numerical Methods for Partial Differential Equations 17 (2) 152 (2001)
DOI: 10.1002/1098-2426(200103)17:2<152::AID-NUM5>3.0.CO;2-A
See this article

Positivity of Runge-Kutta and diagonally split Runge-Kutta methods

Zoltán Horváth
Applied Numerical Mathematics 28 (2-4) 309 (1998)
DOI: 10.1016/S0168-9274(98)00050-6
See this article

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)
DOI: 10.1016/S0898-1221(98)00097-2
See this article

Consistency and stability for some nonnegativity-conserving methods

Zoltán Horváth
Applied Numerical Mathematics 13 (5) 371 (1993)
DOI: 10.1016/0168-9274(93)90095-9
See this article

Contractivity-preserving implicit linear multistep methods

H. W. J. Lenferink
Mathematics of Computation 56 (193) 177 (1991)
DOI: 10.1090/S0025-5718-1991-1052098-0
See this article

Contractivity of Runge-Kutta methods

J. F. B. M. Kraaijevanger
BIT 31 (3) 482 (1991)
DOI: 10.1007/BF01933264
See this article

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)
DOI: 10.1007/BF01931665
See this article

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)
DOI: 10.1002/nme.1620300207
See this article

Contractivity preserving explicit linear multistep methods

H. W. J. Lenferink
Numerische Mathematik 55 (2) 213 (1989)
DOI: 10.1007/BF01406515
See this article

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)
DOI: 10.1002/nme.1620280503
See this article

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)
DOI: 10.1016/0377-0427(87)90126-9
See this article

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

J. F. B. M. Kraaijevanger
Numerische Mathematik 48 (3) 303 (1986)
DOI: 10.1007/BF01389477
See this article

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)
DOI: 10.1007/BF01389539
See this article

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)
DOI: 10.1137/0516076
See this article

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)
DOI: 10.1007/BF02576537
See this article

On the relation between stability and contractivity

M. N. Spijker
BIT 24 (4) 656 (1984)
DOI: 10.1007/BF01934922
See this article

Instability in Runge-Kutta schemes for simulation of oil recovery

P. H. Sammon and P. Forsyth
BIT Numerical Mathematics 24 (3) 373 (1984)
DOI: 10.1007/BF02136036
See this article

Contractivity in the numerical solution of initial value problems

M. N. Spijker
Numerische Mathematik 42 (3) 271 (1983)
DOI: 10.1007/BF01389573
See this article

The use of positive matrices for the analysis of the large time behavior of the numerical solution of reaction-diffusion systems

Luciano Galeone
Mathematics of Computation 41 (164) 461 (1983)
DOI: 10.1090/S0025-5718-1983-0717696-5
See this article

A discrete method for the identification of parameters of a deterministic epidemic model

Giovanni di Lena and Gabriella Serio
Mathematical Biosciences 60 (2) 161 (1982)
DOI: 10.1016/0025-5564(82)90127-4
See this article