Publications

2018

Journal Articles

A. Abdulle; I. Almuslimani; G. Vilmart : Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations; SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION. 2018. DOI : 10.1137/17M1145859.
A. Abdulle; M. Grote; O. Jecker : Finite element heterogeneous multiscale method for elastic waves in heterogeneous media; COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 2018. DOI : 10.1016/j.cma.2018.01.038.
D. Arjmand; M. Poluektov; G. Kreiss : Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature; ADVANCES IN COMPUTATIONAL MATHEMATICS. 2018. DOI : 10.1007/s10444-017-9575-3.
A. Abdulle; G. Rosilho De Souza : A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations. 2018.
A. Abdulle; A. Di Blasio : A Bayesian numerical homogenization method for elliptic multiscale inverse problems; publication. 2018.
A. Abdulle; T. N. Pouchon : Effective Models for Long Time Wave Propagation in Locally Periodic Media; SIAM Journal on Numerical Analysis. 2018. DOI : 10.1137/17M113678X.

2017

Journal Articles

A. Abdulle; G. Garegnani : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration; publication. 2017.
A. Abdulle; M. J. Grote; O. Jecker : FE-HMM for elastic waves in heterogeneous media; publication. 2017.
A. Abdulle; I. Almuslimani; G. Vilmart : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations; publication. 2017.
A. Abdulle; G. A. Pavliotis; U. Vaes : Spectral methods for multiscale stochastic differential equations; SIAM/ASA Journal on Uncertainty Quantification. 2017. DOI : 10.1137/16M1094117.
A. Abdulle; M. E. Huber; S. Lemaire : An optimization-based numerical method for diffusion problems with sign-changing coefficients; C. R. Acad. Sci. Paris, Série I. 2017. DOI : 10.1016/j.crma.2017.02.010.
A. Abdulle; O. Budác; A. Imboden : Multiscale methods and model order reduction for flow problems in three-scale porous media; Journal of Computational Physics. 2017.
A. Abdulle; O. C. Jecker : On heterogeneous coupling of multiscale methods for problems with and without scale separation; Research in the mathematical Sciences. 2017. DOI : 10.1186/s40687-017-0118-9.
A. Abdulle; P. Henning : Multiscale methods for wave problems in heterogenous media; Handbook of Numerical Analysis. 2017.
A. Abdulle; M. E. Huber : Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows; Numerische Mathematik. 2017. DOI : 10.1007/s00211-016-0854-6.
A. Abdulle; O. Budác : A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media; Siam Journal on Scientific Computing. 2017. DOI : 10.1137/15M1050690.
A. Abdulle; P. Henning : Localized orthogonal decomposition method for the wave equation with a continuum of scales; Mathematics of Computation. 2017. DOI : 10.1090/mcom/3114.

Theses

T. N. Pouchon : Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7881.
O. C. Jecker : Optimization based methods for highly heterogeneous multiscale problems and multiscale methods for elastic waves. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7467.

2016

Journal Articles

A. Abdulle; O. C. Jecker; A. Shapeev : An Optimization Based Coupling Method For Multiscale Problems; Multiscale Modeling & Simulation. 2016. DOI : 10.1137/15M105389X.
A. Abdulle; M. E. Huber : Finite Element Heterogeneous Multiscale Method For Nonlinear Monotone Parabolic Homogenization Problems; Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique. 2016. DOI : 10.1051/m2an/2016003.
A. Abdulle; A. Di Blasio : Numerical homogenization and model order reduction for multiscale inverse problems; publication. 2016.
A. Abdulle; O. Budác : Multiscale model reduction methods for flow in heterogeneous porous media; publication. 2016.
A. Abdulle; T. N. Pouchon : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization; Mathematical Models and Methods in Applied Sciences. 2016. DOI : 10.1142/S0218202516500627.
A. Abdulle : Numerical homogenization methods for parabolic monotone problems; Springer, Lecture Notes in Computational Science and Engineering. 2016.
A. Abdulle; O. Budác : A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media; Computer Methods in Applied Mechanics and Engineering. 2016. DOI : 10.1016/j.cma.2016.03.016.
A. Abdulle; T. N. Pouchon : A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time; SIAM Journal on Numerical Analysis. 2016. DOI : 10.1137/15M1025633.
A. Abdulle; M. E. Huber : Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization; Numerical Methods for Partial Differential Equations. 2016. DOI : 10.1002/num.22037.

Conference Papers

A. Abdulle : Numerical methods for wave equation in heterogenous media. 2016. Oberwolfach Workshop, Oberwolfach, March 20-26, 2016.
A. Abdulle; O. C. Jecker : Numerical experiments for multiscale problems in linear elasticity. 2016. Numerical Mathematics and Advanced Applications ‐ ENUMATH 2015, Ankara.

Theses

O. Budáč : Multiscale methods for Stokes flow in heterogeneous media. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7135.

2015

Journal Articles

A. Abdulle; O. Budác : A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries; Comptes Rendus Mathematique. 2015. DOI : 10.1016/j.crma.2015.03.019.
A. Abdulle : The role of numerical integration in numerical homogenization; ESAIM: Proceedings. 2015.
A. Abdulle; P. Henning : A reduced basis localized orthogonal decomposition; Journal of Computational Physics. 2015. DOI : 10.1016/j.jcp.2015.04.016.
A. Abdulle; M. E. Huber; G. Vilmart : Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems; Multiscale Modeling and Simulation. 2015. DOI : 10.1137/140975504.
A. Abdulle; O. C. Jecker : An optimization-based multiscale coupling method; Communication in Mathematical Sciences. 2015. DOI : 10.4310/CMS.2015.v13.n6.a13.
A. Abdulle; G. Vilmart; K. C. Zygalakis : Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics; SIAM Journal on Numerical Analysis. 2015. DOI : 10.1137/140962644.
A. Abdulle; O. Budác : An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media; Multiscale Modeling and Simulation. 2015. DOI : 10.1137/130950136.
A. Abdulle; Y. Bai; G. Vilmart : Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems; Discrete and Continuous Dynamical Systems. 2015. DOI : 10.3934/dcdss.2015.8.91.
A. Abdulle; Y. Bai : Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales; IMA, Journal of Numerical Analysis. 2015. DOI : 10.1093/imanum/drt066.

Conference Papers

A. Abdulle : Reduced basis heterogeneous multiscale methods. 2015. Euromech Colloquium 559 - Multi-scale computational methods for bridging scales in materials and structures, Eindhoven, The Netherlands, February 23-25, 2015.
A. Abdulle : Reduced basis techniques for multiscale methods. 2015. Oberwolfach Workshop, Oberwolfach, January 11-17, 2015.
A. Abdulle; O. Budác : Multiscale adaptive method for Stokes fow in heterogenenous media. 2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.
A. Abdulle; Y. Bai; T. N. Pouchon : Reduced basis numerical homogenization method for the multiscale wave equation. 2015. Enumath 2013, EPFL,Lausanne, Switzerland, August 26-30,2013. p. 397-405.
A. Abdulle; A. Blumenthal : Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. 2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.

Theses

A. Blumenthal : Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6771.
M. E. Huber : Numerical homogenization methods for advection-diffusion and nonlinear monotone problems with multiple scales. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6769.

Book Chapters

A. Abdulle : Numerical homogenization; Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 1066-1074.
A. Abdulle : Explicit stabilized Runge-Kutta methods; Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 460-468.

Conference Proceedings

A. Abdulle; S. Deparis; D. Kressner; F. Nobile; M. Picasso : Numerical Mathematics and Advanced Applications - ENUMATH 2013. 2015.

2014

Journal Articles

P. Henning; A. Malqvist; D. Peterseim : Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates; Siam Journal On Numerical Analysis. 2014. DOI : 10.1137/130921520.
A. Abdulle; M. E. Huber : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems; publication. 2014.
A. Abdulle; Y. Bai : Reduced order modelling numerical homogenization; Philosophical Transactions of the Royal Society A. 2014. DOI : 10.1098/rsta.2013.0388.
A. Abdulle; M. J. Grote; C. Stohrer : Finite element heterogeneous multiscale method for the wave equation: long-time effects; Multiscale Modeling and Simulation. 2014. DOI : 10.1137/13094195X.
A. Abdulle; G. Vilmart; K. C. Zygalakis : High order numerical approximation of the invariant measure of ergodic SDEs; Siam Journal on Numerical Analysis. 2014. DOI : 10.1137/130935616.
A. Abdulle; Y. Bai; G. Vilmart : An online-offline homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems; International Journal for Numerical Methods in Engineering. 2014. DOI : 10.1002/nme.4682.
A. Abdulle; M. E. Huber : Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales; Numerische Mathematik. 2014. DOI : 10.1007/s00211-013-0578-9.
A. Abdulle; G. Vilmart : Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems; Mathematics of Computation. 2014. DOI : 10.1090/S0025-5718-2013-02758-5.

Conference Papers

A. Abdulle : Numerical techniques for differential equations with multiple scales in space or time. 2014. Oberwolfach Workshop, Oberwolfach. p. 48-50.
A. Abdulle : Numerical methods for multiscale parabolic and hyperbolic problems. 2014. Oberwolfach Workshop, Oberwolfach. p. 1631-1633.

2013

Journal Articles

A. Abdulle; M. J. Grote; C. Stohrer : FE heterogeneous multiscale method for long time wave propagation; Comptes Rendus Mathématique (Académie des Sciences). 2013. DOI : 10.1016/j.crma.2013.06.002.
A. Abdulle; A. Blumenthal : Stabilized multilevel Monte Carlo method for stiff stochastic differential equations; Journal of Computational Physics. 2013. DOI : 10.1016/j.jcp.2013.05.039.
A. Abdulle; G. Vilmart; K. Zygalakis : Weak second order explicit stabilized methods for stiff stochastic differential equations; SIAM Journal on Scientific Computing. 2013. DOI : 10.1137/12088954X.
A. Abdulle; Y. Bai : Adaptive reduced basis finite element heterogeneous multiscale method; Computer Methods in Applied Mechanics and Engineering. 2013. DOI : 10.1016/j.cma.2013.01.002.
A. Abdulle; G. Vilmart; K. Zygalakis : Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations; BIT Numerical Mathematics. 2013. DOI : 10.1007/s10543-013-0430-8.
A. Abdulle; A. Barth; C. Schwab : Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs; SIAM Multiscale Modeling & Simulation. 2013. DOI : 10.1137/120894725.
A. Abdulle; G. Vilmart : PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise; Journal of Computational Physics. 2013. DOI : 10.1016/j.jcp.2013.02.009.
A. Abdulle; P. Lin; A. Shapeev : A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices; SIAM, Journal on Numerical Analysis. 2013. DOI : 10.1137/120894300.
A. Abdulle; A. Nonnenmacher : A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method; Numerical Methods for Partial Differential Equations. 2013. DOI : 10.1002/num.21769.

Conference Papers

A. Abdulle : Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems. 2013. Oberwolfach Workshop onInterplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, March 17-23, 2013. p. 807-809. DOI : 10.4171/OWR/2013/14.
A. Abdulle; M. J. Grote; C. M. Stohrer : Finite element heterogeneous multiscale method for the wave equation: dispersive effects. 2013. 11th International Conference on the Mathematical and Numerical Aspects of Waves.

Theses

Y. Bai : Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems. Lausanne, EPFL, 2013. DOI : 10.5075/epfl-thesis-5922.

2012

Journal Articles

A. Abdulle; Y. Bai : Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems; Journal of Computational Physics. 2012. DOI : 10.1016/j.jcp.2012.02.019.
A. Abdulle; P. Lin; A. Shapeev : Numerical methods for multilattices; SIAM, Multiscale Modeleling Simulation. 2012. DOI : 10.1137/110841163.
A. Abdulle; D. Cohen; G. Vilmart; K. Zygalakis : High weak order methods for stochastic equations based on modified equations; SIAM Journal of Scientific Computing. 2012. DOI : 10.1137/110846609.
A. Abdulle; W. E.; B. Engquist; E. Vanden-Eijnden : The heterogeneous multiscale method; Acta Numerica. 2012. DOI : 10.1017/S0962492912000025.
A. Abdulle : Explicit methods for stiff stochastic differential equations; Lecture Notes in Computational Science and Engineering, Springer. 2012. DOI : 10.1007/978-3-642-21943-6_1.
Y. Hu; A. Abdulle; T. Li : Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size; Communications in Computational Physics. 2012. DOI : 10.4208/cicp.190411.301111a.
A. Abdulle : Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales; Mathematics of Computation. 2012. DOI : 10.1090/S0025-5718-2011-02527-5.
A. Abdulle; G. Vilmart : Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis; Mathematical Models & Methods in Applied Sciences. 2012. DOI : 10.1142/S0218202512500029.
A. Abdulle; G. A. Pavliotis : Numerical methods for stochastic partial differential equations with multiple scales; Journal of Computational Physics. 2012. DOI : 10.1016/j.jcp.2011.11.039.
A. Abdulle; G. Vilmart : A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems; Numerische Mathematik. 2012. DOI : 10.1007/s00211-011-0438-4.

Conference Papers

A. Abdulle : Explicit stabilized integration of stiff determinisitic or stochastic problems. 2012. AIP Conference Proceedings, vol. 1479, p.11-15. p. 11-15. DOI : 10.1063/1.4756050.

Student Projects

J. Rochat : An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction ; 2012.

2011

Journal Articles

A. Abdulle : A priori and a posteriori error analysis for numerical homogenization: a unified framework; Series in Contemporary Applied Mathematics, CAM. 2011.
A. Abdulle; M. J. Grote : Finite element heterogeneous multiscale method for the wave equation; SIAM, Multiscale Modeling & Simulation. 2011. DOI : 10.1137/100800488.
A. Abdulle; G. Vilmart : The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods; Comptes Rendus Mathématique, (Académie des Sciences). 2011. DOI : 10.1016/j.crma.2011.09.005.
A. Abdulle; A. Nonnenmacher : Adaptive finite element heterogeneous multiscale method for homogenization problems; Computer Methods in Applied Mechanics and Engineering. 2011. DOI : 10.1016/j.cma.2010.06.012.

Conference Papers

A. Abdulle; M. J. Grote; C. Stohrer : Finite element heterogeneous multiscale method for transient wave propagation. 2011. 10th International Conference on the Mathematical and Numerical Aspects of Waves, The Pacific Institute for the Mathematical Sciences, 2011.
A. Abdulle : On the efficiency of numerical homogenization methods. 2011. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach, March 20-26, 2011. p. 857-859. DOI : 10.4171/OWR/2011/16.

Theses

A. Nonnenmacher : Adaptive Finite Element Methods for Multiscale Partial Differential Equations. Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-5097.

Reports

A. Abdulle; A. Blumenthal; E. Buckwar : The multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes. 2011.

Student Projects

J. Rochat : Splitting Methods with Modified Potentials and Application to the Damped Wave Equation ; 2011.

2010

Journal Articles

A. Abdulle; A. Nonnenmacher : Erratum to “A short and versatile finite element multiscale code for homogenization problems” [Comput. Methods Appl. Mech. Engrg. 198 (2009) 2839–2859]; Computer Methods in Applied Mechanics and Engineering. 2010. DOI : 10.1016/j.cma.2009.11.020.
P. Chartier; E. Hairer; G. Vilmart : Algebraic Structures of B-series; Foundations Of Computational Mathematics. 2010. DOI : 10.1007/s10208-010-9065-1.
A. Abdulle; Y. Hu; T. Li : Chebyshev methods with discrete noise: the tau-ROCK methods; Journal of Computational Mathematics. 2010. DOI : 10.4208/jcm.2009.10-m1004.
A. Abdulle; A. Nonnenmacher : A short and versatile finite element multiscale code for homogenization problems (vol 198, pg 2839, 2009); Computer Methods In Applied Mechanics And Engineering. 2010. DOI : 10.1016/j.cma.2009.11.020.

Reports

A. Abdulle; A. Shapeev; P. Lin : Homogenization-based analysis of quasicontinuum method for complex crystals. 2010.

2009

Journal Articles

A. Abdulle : The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs; GAKUTO International Series Mathematical Sciences and Applications. 2009.
A. Abdulle; A. Nonnenmacher : A short and versatile finite element multiscale code for homogenization problems; Computer Methods in Applied Mechanics and Engineering. 2009. DOI : 10.1016/j.cma.2009.03.019.
A. Abdulle; A. Nonnenmacher : A posteriori error analysis of the heterogeneous multiscale method for homogenization problems; Comptes Rendus Mathematique. 2009. DOI : 10.1016/j.crma.2009.07.004.

2008

Journal Articles

A. Abdulle; S. Attinger : Effective velocity for transport in heterogeneous compressible flows with mean drift; Physics of Fluids. 2008. DOI : 10.1063/1.2827584.
A. Abdulle; T. Li : S-ROCK methods for stiff Itô SDEs; Communications in Mathematical Sciences. 2008. DOI : 10.4310/CMS.2008.v6.n4.a3.
T. Li; A. Abdulle; W. E. : Effectiveness of implicit methods for stiff stochastic differential equations; Communication in Computational Physics. 2008.
A. Abdulle; S. Cirilli : S-ROCK: Chebyshev methods for stiff stochastic differential equations; SIAM Journal on Scientific Computing. 2008. DOI : 10.1137/070679375.
A. Abdulle : Multiscale method based on discontinuous Galerkin methods for homogenization problems; Comptes Rendus Mathématique (Académie des Sciences). 2008. DOI : 10.1016/j.crma.2007.11.029.

2007

Journal Articles

A. Abdulle; B. Engquist : Finite element heterogeneous multiscale methods with near optimal computational complexity; SIAM Multiscale modeling & simulation. 2007. DOI : 10.1137/060676118.
A. Abdulle; S. Cirilli : Stabilized methods for stiff stochastic systems; Comptes Rendus Mathématique (Académie des Sciences). 2007. DOI : 10.1016/j.crma.2007.10.009.

2006

Journal Articles

A. Abdulle; S. Attinger : Numerical methods for transport problems in microdevices; Large-scale scientific computing. 2006. DOI : 10.1007/11666806_6.
A. Abdulle : Heterogeneous multiscale methods with quadrilateral finite elements; Numerical Mathematics and Advanced Applications. 2006. DOI : 10.1007/978-3-540-34288-5_72.
A. Abdulle : Analysis of a heterogeneous multiscale FEM for problems in elasticity; Mathematical Models & Methods in Applied Sciences. 2006. DOI : 10.1142/S0218202506001285.

Conference Papers

A. Abdulle : Numerical methods for multiscale problems. 2006. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach-Walke, March 19-25, 2006. p. 834-837. DOI : 10.4171/OWR/2006/14.

2005

Journal Articles

A. Abdulle; C. Schwab : Heterogeneous multiscale FEM for diffusion problems on rough surfaces; SIAM Multiscale modeling & simulation. 2005. DOI : 10.1137/030600771.
A. Abdulle : Multiscale methods for advection-diffusion problems; Discrete and Continuous Dynamical Systems Series A. 2005. DOI : 10.3934/proc.2005.2005.11.
A. Abdulle : On a priori error analysis of fully discrete heterogeneous multiscale FEM; SIAM Multiscale modeling & simulation. 2005. DOI : 10.1137/040607137.

Conference Papers

A. Abdulle : Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays. 2005. Oberwolfach Workshop on Reactive Flow and Transport Through Complex Systems, Oberwolfach-Walke, October 30 – November 5, 2005. p. 2769-2771. DOI : 10.4171/OWR/2005/49.

2004

Journal Articles

A. Abdulle; S. Attinger : Homogenization method for transport of DNA particles in heterogeneous arrays; Multiscale modelling and simulation. 2004. DOI : 10.1007/978-3-642-18756-8_2.

Conference Papers

A. Abdulle : Solving diffusions problems on rough surfaces with a hierarchical Multiscale FEM. 2004. Proceedings in Applied Mathematics and Mechanics, vol. 4, num. 1, p. 694-695, 2004. p. 694-695.

2003

Journal Articles

A. Abdulle; W. E. : Finite difference heterogeneous multi-scale method for homogenization problems; Journal of Computational Physics. 2003. DOI : 10.1016/S0021-9991(03)00303-6.

Conference Papers

A. Abdulle : Solving multi-scale problems with heterogeneous finite difference methods. 2003. Proceedings in Applied Mathematics and Mechanics, vol.3, num. 1, p. 575-576, 2003. p. 575-576.

2002

Journal Articles

A. Abdulle; G. Wanner : 200 years of least squares method; Pokroky Mat. Fyz. Astron.. 2002. DOI : 10.1007/PL00000559.
A. Abdulle : Fourth order Chebyshev methods with recurrence relation; SIAM Journal on Scientific Computing. 2002. DOI : 10.1137/S1064827500379549.

Conference Papers

A. Abdulle : Large stiff systems solved by Chebyshev methods. 2002. Proceedings in Applied Mathematics and Mechanics, vol.1, num. 1, p. 508-509, 2002. p. 508-509.

2001

Journal Articles

A. Abdulle; A. A. Medovikov : Second order Chebyshev methods based on orthogonal polynomials; Numerische Mathematik. 2001. DOI : 10.1007/s002110100292.

2000

Journal Articles

A. Abdulle : On roots and error constants of optimal stability polynomials; BIT : Numerical Mathematics. 2000. DOI : 10.1023/A:1022378621048.