Single step methods for inhomogeneous linear differential equations in Banach space
RAIRO. Anal. numér., 16 1 (1982) 5-26
Published online: 2017-01-31
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):
Optimizing Coarse Propagators in Parareal Algorithms
Bangti Jin, Qingle Lin and Zhi ZhouSIAM Journal on Scientific Computing 47 (2) A735 (2025)
https://doi.org/10.1137/23M1619733
A fast third order algorithm for two dimensional inhomogeneous fractional parabolic partial differential equations
M. Yousuf and Shahzad SarwarInternational Journal of Computer Mathematics 101 (1) 1 (2024)
https://doi.org/10.1080/00207160.2023.2279511
Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge–Kutta discontinuous Galerkin method
Zheng SunMathematics of Computation (2024)
https://doi.org/10.1090/mcom/4037
Robust Convergence of Parareal Algorithms with Arbitrarily High-Order Fine Propagators
Jiang Yang, Zhaoming Yuan and Zhi ZhouSSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4097528
A Fourth-Order Time-Stepping Method for Two-Dimensional, Distributed-Order, Space-Fractional, Inhomogeneous Parabolic Equations
Muhammad Yousuf, Khaled M. Furati and Abdul Q. M. KhaliqFractal and Fractional 6 (10) 592 (2022)
https://doi.org/10.3390/fractalfract6100592
Error Analysis of Multirate Leapfrog-Type Methods for Second-Order Semilinear Odes
Constantin Carle and Marlis HochbruckSIAM Journal on Numerical Analysis 60 (5) 2897 (2022)
https://doi.org/10.1137/21M1427255
Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations
Jiang Yang, Zhaoming Yuan and Zhi ZhouJournal of Scientific Computing 90 (2) (2022)
https://doi.org/10.1007/s10915-021-01746-y
The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing
H. Ghafouri, M. Ranjbar and A. KhaniComputational Economics 56 (4) 695 (2020)
https://doi.org/10.1007/s10614-019-09927-6
Energy-corrected FEM and explicit time-stepping for parabolic problems
Piotr Swierczynski and Barbara WohlmuthESAIM: Mathematical Modelling and Numerical Analysis 53 (6) 1893 (2019)
https://doi.org/10.1051/m2an/2019038
Unified error analysis for nonconforming space discretizations of wave-type equations
David Hipp, Marlis Hochbruck and Christian StohrerIMA Journal of Numerical Analysis 39 (3) 1206 (2019)
https://doi.org/10.1093/imanum/dry036
Avoiding order reduction when integrating linear initial boundary value problems with exponential splitting methods
I Alonso-Mallo, B Cano and N RegueraIMA Journal of Numerical Analysis 38 (3) 1294 (2018)
https://doi.org/10.1093/imanum/drx047
First-Order Partial Differential Equation with a Nonlocal Boundary Condition
Abdullah S. Erdogan and Sueda N. TekalanNumerical Functional Analysis and Optimization 38 (10) 1373 (2017)
https://doi.org/10.1080/01630563.2017.1317002
Implicit Runge--Kutta Methods and Discontinuous Galerkin Discretizations for Linear Maxwell's Equations
Marlis Hochbruck and Tomislav PažurSIAM Journal on Numerical Analysis 53 (1) 485 (2015)
https://doi.org/10.1137/130944114
Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws
Willem Hundsdorfer, David I. Ketcheson and Igor SavostianovJournal of Scientific Computing 63 (3) 633 (2015)
https://doi.org/10.1007/s10915-014-9906-1
Finite-difference method for the hyperbolic system of equations with nonlocal boundary conditions
Allaberen Ashyralyev and Rahat PrenovAdvances in Difference Equations 2014 (1) (2014)
https://doi.org/10.1186/1687-1847-2014-26
Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems
A. Arrarás, L. Portero and I. YotovJournal of Computational Physics 257 1321 (2014)
https://doi.org/10.1016/j.jcp.2013.08.013
A-stable Runge–Kutta methods for semilinear evolution equations
Marcel Oliver and Claudia WulffJournal of Functional Analysis 263 (7) 1981 (2012)
https://doi.org/10.1016/j.jfa.2012.06.022
Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
Georgios Akrivis, Charalambos Makridakis and Ricardo H. NochettoNumerische Mathematik 118 (3) 429 (2011)
https://doi.org/10.1007/s00211-011-0363-6
Extrapolated Implicit-Explicit Time Stepping
Emil M. Constantinescu and Adrian SanduSIAM Journal on Scientific Computing 31 (6) 4452 (2010)
https://doi.org/10.1137/080732833
A posteriori error estimates by recovered gradients in parabolic finite element equations
D. Leykekhman and L. B. WahlbinBIT Numerical Mathematics 48 (3) 585 (2008)
https://doi.org/10.1007/s10543-008-0169-9
Pricing exotic options with L-stable Padé schemes
A.Q.M. Khaliq, D.A. Voss and M. YousufJournal of Banking & Finance 31 (11) 3438 (2007)
https://doi.org/10.1016/j.jbankfin.2007.04.012
IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
Willem Hundsdorfer and Steven J. RuuthJournal of Computational Physics 225 (2) 2016 (2007)
https://doi.org/10.1016/j.jcp.2007.03.003
High order smoothing schemes for inhomogeneous parabolic problems with applications in option pricing
A.Q.M. Khaliq, B.A. Wade, M. Yousuf and J. Vigo‐AguiarNumerical Methods for Partial Differential Equations 23 (5) 1249 (2007)
https://doi.org/10.1002/num.20228
Linear Discrete Parabolic Problems
North-Holland Mathematics Studies, Linear Discrete Parabolic Problems 203 269 (2006)https://doi.org/10.1016/S0304-0208(06)80053-8
Fast Runge-Kutta approximation of inhomogeneous parabolic equations
María López-Fernández, Christian Lubich, Cesar Palencia and Achim SchädleNumerische Mathematik 102 (2) 277 (2005)
https://doi.org/10.1007/s00211-005-0624-3
A posteriorierror estimates for a nonconforming finite element discretization of the heat equation
Serge Nicaise and Nadir SoualemESAIM: Mathematical Modelling and Numerical Analysis 39 (2) 319 (2005)
https://doi.org/10.1051/m2an:2005009
Smoothing with positivity‐preserving Padé schemes for parabolic problems with nonsmooth data
B. A. Wade, A. Q. M. Khaliq, M. Siddique and M. YousufNumerical Methods for Partial Differential Equations 21 (3) 553 (2005)
https://doi.org/10.1002/num.20039
Convergence of Runge–Kutta methods applied to linear partial differential-algebraic equations
K. Debrabant and K. StrehmelApplied Numerical Mathematics 53 (2-4) 213 (2005)
https://doi.org/10.1016/j.apnum.2004.08.023
Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions
I. Alonso-Mallo, B. Cano and J. JorgeMathematics of Computation 73 (248) 1801 (2004)
https://doi.org/10.1090/S0025-5718-04-01660-6
Optimal orders of convergence for Runge–Kutta methods and linear, initial boundary value problems
I. Alonso-Mallo and C. PalenciaApplied Numerical Mathematics 44 (1-2) 1 (2003)
https://doi.org/10.1016/S0168-9274(02)00110-1
Computational Science and Its Applications — ICCSA 2003
D. A. Voss, A. Q. M. Khaliq, S. H. K. Kazmi and H. HeLecture Notes in Computer Science, Computational Science and Its Applications — ICCSA 2003 2669 199 (2003)
https://doi.org/10.1007/3-540-44842-X_21
Accuracy and stability of splitting with Stabilizing Corrections
Willem HundsdorferApplied Numerical Mathematics 42 (1-3) 213 (2002)
https://doi.org/10.1016/S0168-9274(01)00152-0
Numerical Analysis: Historical Developments in the 20th Century
Vidar ThoméeNumerical Analysis: Historical Developments in the 20th Century 361 (2001)
https://doi.org/10.1016/B978-0-444-50617-7.50016-1
From finite differences to finite elements
Vidar ThoméeJournal of Computational and Applied Mathematics 128 (1-2) 1 (2001)
https://doi.org/10.1016/S0377-0427(00)00507-0
Subgrid stabilization of Galerkin approximations of linear contraction semi-groups of classC0 in Hilbert spaces
Jean-Luc GuermondNumerical Methods for Partial Differential Equations 17 (1) 1 (2001)
https://doi.org/10.1002/1098-2426(200101)17:1<1::AID-NUM1>3.0.CO;2-1
Partial Differential Equations
Vidar ThoméePartial Differential Equations 1 (2001)
https://doi.org/10.1016/B978-0-444-50616-0.50004-X
Rational methods with optimal order of convergence for partial differential equations
Isaías Alonso-MalloApplied Numerical Mathematics 35 (4) 265 (2000)
https://doi.org/10.1016/S0168-9274(99)00144-0
Trapezoidal and midpoint splittings for initial-boundary value problems
Willem HundsdorferMathematics of Computation 67 (223) 1047 (1998)
https://doi.org/10.1090/S0025-5718-98-00984-3
The Correct Formulation of Intermediate Boundary Conditions for Runge--Kutta Time Integration of Initial Boundary Value Problems
D. PathriaSIAM Journal on Scientific Computing 18 (5) 1255 (1997)
https://doi.org/10.1137/S1064827594273948
Time-stepping algorithms for semidiscretized linear parabolic PDEs based on rational approximants with distinct real poles
D. A. Voss and A. Q. M. KhaliqAdvances in Computational Mathematics 6 (1) 353 (1996)
https://doi.org/10.1007/BF02127713
Well-posed solvability of the Cauchy problem for difference equations of parabolic type
Allaberen Ashyralyev and Pavel Evseyevich SobolevskiiNonlinear Analysis: Theory, Methods & Applications 24 (2) 257 (1995)
https://doi.org/10.1016/0362-546X(94)E0004-Z
Resolvent estimates for elliptic finite element operators in one dimension
M. Crouzeix, S. Larsson and V. ThoméeMathematics of Computation 63 (207) 121 (1994)
https://doi.org/10.1090/S0025-5718-1994-1242058-1
On fully discrete Galerkin approximations for partial integro-differential equations of parabolic type
Nai Ying ZhangMathematics of Computation 60 (201) 133 (1993)
https://doi.org/10.1090/S0025-5718-1993-1149295-4
Runge-Kutta methods for parabolic equations and convolution quadrature
Ch. Lubich and A. OstermannMathematics of Computation 60 (201) 105 (1993)
https://doi.org/10.1090/S0025-5718-1993-1153166-7
On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation
Ohannes Karakashian, Georgios D. Akrivis and Vassilios A. DougalisSIAM Journal on Numerical Analysis 30 (2) 377 (1993)
https://doi.org/10.1137/0730018
Runge-Kutta methods for partial differential equations and fractional orders of convergence
A. Ostermann and M. RocheMathematics of Computation 59 (200) 403 (1992)
https://doi.org/10.1090/S0025-5718-1992-1142285-6
Unconditional convergence of some Crank-Nicolson LOD methods for initial-boundary value problems
Willem HundsdorferMathematics of Computation 58 (197) 35 (1992)
https://doi.org/10.1090/S0025-5718-1992-1106972-8
A Scheme for Parallelizing Certain Algorithms for the Linear Inhomogeneous Heat Equation
Steven M. SerbinSIAM Journal on Scientific and Statistical Computing 13 (2) 449 (1992)
https://doi.org/10.1137/0913024
Error estimates for the numerical solution of a time-periodic linear parabolic problem
Anita HansboBIT 31 (4) 664 (1991)
https://doi.org/10.1007/BF01933180
On error structures and extrapolation for stiff systems, with application in the method of lines
W. AuzingerComputing 44 (4) 331 (1990)
https://doi.org/10.1007/BF02241272
Stability and convergence at the PDE/stiff ode interface
J.M. Sanz-Serna and J.G. VerwerApplied Numerical Mathematics 5 (1-2) 117 (1989)
https://doi.org/10.1016/0168-9274(89)90028-7
Convergence analysis of one-step schemes in the method of lines
J.M. Sanz-Serna and J.G. VerwerApplied Mathematics and Computation 31 183 (1989)
https://doi.org/10.1016/0096-3003(89)90118-5
Upper semicontinuity of attractors for approximations of semigroups and partial differential equations
Jack K. Hale, Xiao-Biao Lin and Geneviève RaugelMathematics of Computation 50 (181) 89 (1988)
https://doi.org/10.1090/S0025-5718-1988-0917820-X
Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations
J. M. Sanz-Serna, J. G. Verwer and W. H. HundsdorferNumerische Mathematik 50 (4) 405 (1986)
https://doi.org/10.1007/BF01396661
Finite element solution of diffusion problems with irregular data
Rolf RannacherNumerische Mathematik 43 (2) 309 (1984)
https://doi.org/10.1007/BF01390130
On the relation between stability and contractivity
M. N. SpijkerBIT 24 (4) 656 (1984)
https://doi.org/10.1007/BF01934922
Galerkin Finite Element Methods for Parabolic Problems
Lecture Notes in Mathematics, Galerkin Finite Element Methods for Parabolic Problems 1054 106 (1984)https://doi.org/10.1007/BFb0071798