• Previous Article
    Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces
  • DCDS Home
  • This Issue
  • Next Article
    On a class of elliptic and parabolic equations in convex domains without boundary conditions
December  2008, 22(4): 955-972. doi: 10.3934/dcds.2008.22.955

A functional calculus approach for the rational approximation with nonuniform partitions


Laboratoire de Mathématiques et Applications, Université de Poitiers & CNRS, Téléport 2 - BP 30179, 86 962 Futuroscope Chasseneuil Cedex, France, France

Received  September 2007 Revised  November 2007 Published  September 2008

By introducing $M$-functional calculus we generalize some results of Brenner and Thomée on the stability and convergence of rational approximation schemes of bounded semigroups for nonuniform time steps. We give also the rate of convergence for the approximation of the time derivative of these semigroups.
Citation: Hassan Emamirad, Arnaud Rougirel. A functional calculus approach for the rational approximation with nonuniform partitions. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 955-972. doi: 10.3934/dcds.2008.22.955

Allaberen Ashyralyev. Well-posedness of the modified Crank-Nicholson difference schemes in Bochner spaces. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 29-51. doi: 10.3934/dcdsb.2007.7.29


Armand Bernou. A semigroup approach to the convergence rate of a collisionless gas. Kinetic and Related Models, 2020, 13 (6) : 1071-1106. doi: 10.3934/krm.2020038


Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42.


Ciprian Preda, Petre Preda, Adriana Petre. On the asymptotic behavior of an exponentially bounded, strongly continuous cocycle over a semiflow. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1637-1645. doi: 10.3934/cpaa.2009.8.1637


Xinfu Chen, Bei Hu, Jin Liang, Yajing Zhang. Convergence rate of free boundary of numerical scheme for American option. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1435-1444. doi: 10.3934/dcdsb.2016004


Fabrizio Colombo, Graziano Gentili, Irene Sabadini and Daniele C. Struppa. A functional calculus in a noncommutative setting. Electronic Research Announcements, 2007, 14: 60-68. doi: 10.3934/era.2007.14.60


Vladimir V. Kisil. Mobius transformations and monogenic functional calculus. Electronic Research Announcements, 1996, 2: 26-33.


Zhihua Liu, Pierre Magal. Functional differential equation with infinite delay in a space of exponentially bounded and uniformly continuous functions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2271-2292. doi: 10.3934/dcdsb.2019227


Harun Karsli, Purshottam Narain Agrawal. Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation. Mathematical Foundations of Computing, 2022  doi: 10.3934/mfc.2022002


Sondre Tesdal Galtung. A convergent Crank-Nicolson Galerkin scheme for the Benjamin-Ono equation. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1243-1268. doi: 10.3934/dcds.2018051


Yoshiho Akagawa, Elliott Ginder, Syota Koide, Seiro Omata, Karel Svadlenka. A Crank-Nicolson type minimization scheme for a hyperbolic free boundary problem. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2661-2681. doi: 10.3934/dcdsb.2021153


Yulan Lu, Minghui Song, Mingzhu Liu. Convergence rate and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 695-717. doi: 10.3934/dcdsb.2018203


Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial and Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485


Samir EL Mourchid. On a hypercylicity criterion for strongly continuous semigroups. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 271-275. doi: 10.3934/dcds.2005.13.271


Stephen Thompson, Thomas I. Seidman. Approximation of a semigroup model of anomalous diffusion in a bounded set. Evolution Equations and Control Theory, 2013, 2 (1) : 173-192. doi: 10.3934/eect.2013.2.173


Panagiotis Paraschis, Georgios E. Zouraris. On the convergence of the Crank-Nicolson method for the logarithmic Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022074


Rich Stankewitz. Density of repelling fixed points in the Julia set of a rational or entire semigroup, II. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 2583-2589. doi: 10.3934/dcds.2012.32.2583


Viviana Alejandra Díaz, David Martín de Diego. Generalized variational calculus for continuous and discrete mechanical systems. Journal of Geometric Mechanics, 2018, 10 (4) : 373-410. doi: 10.3934/jgm.2018014


Matania Ben–Artzi, Joseph Falcovitz, Jiequan Li. The convergence of the GRP scheme. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 1-27. doi: 10.3934/dcds.2009.23.1


Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012

2020 Impact Factor: 1.392


  • PDF downloads (69)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]