Applications of Explicit Stabilized Runge-Kutta Methods Homepage
Medicine and biology
Kinjo AR, Takada S. Competition between protein folding and aggregation with
molecular chaperones in crowded solutions: Insight from mesoscopic simulations
BIOPHYS J 85 (6): 3521-3531 DEC 2003
Kinjo AR, Takada S. Effects of macromolecular crowding on protein folding and
aggregation studied by density functional theory: Dynamics PHYS REV E 66 (5):
Art. No. 051902 NOV 2002
Abdulle A, Weinan E Finite difference heterogeneous multi-scale method for
homogenization problems J COMPUT PHYS 191 (1): 18-39 OCT 10 2003
Abdulle A. On roots and error constants of optimal stability polynomials. BIT
40 (1): 177-182 2000
Gear CW, Kevrekidis IG Telescopic projective methods for parabolic differential
equations J COMPUT PHYS 187 (1): 95-109 MAY 1 2003
Gear CW, Kevrekidis IG Projective methods for stiff differential equations:
Problems with gaps in their eigenvalue spectrum SIAM J SCI COMPUT 24 (4):
1091-1106 2003
Filbet F, Pareschi L. A numerical method for the accurate solution of the
Fokker-Planck-Landau equation in the nonhomogeneous case. J COMPUT PHYS 179
(1): 1-26 JUN 10 2002
Kurganov A, Levy D. Central-upwind schemes for the Saint-Venant system.
ESAIM-MATH MODEL NUM 36 (3): 397-425 MAY-JUN 2002
Kurganov A, Petrova G. A third-order semi-discrete genuinely multidimensional
central scheme for hyperbolic conservation laws and related problems. NUMER
MATH 88 (4): 683-729 JUN 2001
Kurganov A, Tadmor E. New high-resolution central schemes for nonlinear
conservation laws and convection-diffusion equations. J COMPUT PHYS 160 (1):
241-282 MAY 1 2000
Lebedev VI. Explicit difference schemes for solving stiff systems of ODEs and
PDEs with complex spectrum. RUSS J NUMER ANAL M 13 (2): 107-116 1998
Lebedev VI, Loutsenko SV, Lykossov VN. Large-eddy simulation of convective
boundary layer using explicit difference schemes. RUSS J NUMER ANAL M 15 (1):
95-110 2000
Valorani M, Goussis DA. Explicit time-scale splitting algorithm for stiff
problems: Auto-ignition of gaseous mixtures behind a steady shock. J COMPUT
PHYS 169 (1): 44-79 MAY 1 2001
Pareschi L, Russo G, Toscani G. Fast spectral methods for the
Fokker-Planck-Landau collision operator. J COMPUT PHYS 165 (1): 216-236 NOV 20
2000
Sommeijer BP, Shampine LF, Verwer JG. RKC: An explicit solver for parabolic
PDEs. J COMPUT APPL MATH 88 (2): 315-326 MAR 2 1998
1. Central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction
Author(s): Liu YJ, Shu CW, Tadmor ET, et al.
Source: SIAM JOURNAL ON NUMERICAL ANALYSIS Volume: 45 Issue: 6 Pages: 2442-2467 Published: 2007
Times Cited: 1
2. Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations
Author(s): Banda M, Klar A, Pareschi L, et al.
Source: MATHEMATICS OF COMPUTATION Volume: 77 Issue: 262 Pages: 943-965 Published: 2008
Times Cited: 1
3. Boundary conditions for a divergence free velocity-pressure formulation of the Navier-Stokes equations
Author(s): Nordstroem J, Mattsson K, Swanson C
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 225 Issue: 1 Pages: 874-890 Published: JUL 1 2007
Times Cited: 3
4. Essentially optimal explicit Runge-Kutta methods with application to hyperbolic-parabolic equations
Author(s): Torrilhon M, Jeltsch R
Source: NUMERISCHE MATHEMATIK Volume: 106 Issue: 2 Pages: 303-334 Published: APR 2007
Times Cited: 0
5. An additive semi-implicit Runge-Kutta family of schemes for nonstiff systems
Author(s): Pantano C
Source: APPLIED NUMERICAL MATHEMATICS Volume: 57 Issue: 3 Pages: 297-303 Published: MAR 2007
Times Cited: 0
6. Second-order accurate projective integrators for multiscale problems
Author(s): Lee SL, Gear CW
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 201 Issue: 1 Pages: 258-274 Published: APR 1 2007
Times Cited: 5
7. An improved algorithm for simulating three-dimensional, viscoelastic turbulence
Author(s): Vaithianathan T, Robert A, Brasseur JG, et al.
Source: JOURNAL OF NON-NEWTONIAN FLUID MECHANICS Volume: 140 Issue: 1-3 Special Issue: Sp. Iss. SI Pages: 3-22 Published: DEC 30 2006
Times Cited: 4
8. Automatic integration of the reaction path using diagonally implicit Runge-Kutta methods
Author(s): Burger SK, Yang WT
Source: JOURNAL OF CHEMICAL PHYSICS Volume: 125 Issue: 24 Article Number: 244108 Published: DEC 28 2006
Times Cited: 1
9. Towards explicit methods for differential algebraic equations
Author(s): Gear CW
Source: BIT NUMERICAL MATHEMATICS Volume: 46 Issue: 3 Pages: 505-514 Published: SEP 2006
Times Cited: 2
10. On a practical implementation of particle methods
Author(s): Chertock A, Kurganov A
Source: APPLIED NUMERICAL MATHEMATICS Volume: 56 Issue: 10-11 Pages: 1418-1431 Published: OCT-NOV 2006
Times Cited: 1
11. A combined explicit-implicit method for high accuracy reaction path integration
Author(s): Burger SK, Yang WT
Source: JOURNAL OF CHEMICAL PHYSICS Volume: 124 Issue: 22 Article Number: 224102 Published: JUN 14 2006
Times Cited: 1
12. An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
Author(s): Erban R, Kevrekidis IG, Othmer HG
Source: PHYSICA D-NONLINEAR PHENOMENA Volume: 215 Issue: 1 Pages: 1-24 Published: MAR 1 2006
Times Cited: 9
13. Modeling low Mach number reacting flow with detailed chemistry and transport
Author(s): Najm HN, Knio OM
Source: JOURNAL OF SCIENTIFIC COMPUTING Volume: 25 Issue: 1 Pages: 263-287 Published: OCT 2005
Times Cited: 6
14.
This record has been added to your Marked List. Variable time steps optimization of L-omega-stable Crank-Nicolson method
Author(s): Medovikov AA, Lebedev VI
Source: RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING Volume: 20 Issue: 3 Pages: 283-303 Published: 2005
Times Cited: 1
15. Central schemes on overlapping cells
Author(s): Liu YJ
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 209 Issue: 1 Pages: 82-104 Published: OCT 10 2005
Times Cited: 7
16. Effective computation of optimal stability polynomials
Author(s): Bogatyrev A
Source: CALCOLO Volume: 41 Issue: 4 Pages: 247-256 Published: 2004
Times Cited: 0
17. On degenerate saturated-diffusion equations with convection
Author(s): Chertock A, Kurganov A, Rosenau P
Source: NONLINEARITY Volume: 18 Issue: 2 Pages: 609-630 Published: MAR 2005
Times Cited: 1
18.
This record has been added to your Marked List. The method of regularized Stokeslets in three dimensions: Analysis, validation, and application to helical swimming
Author(s): Cortez R, Fauci L, Medovikov A
Source: PHYSICS OF FLUIDS Volume: 17 Issue: 3 Article Number: 031504 Published: MAR 2005
Times Cited: 5
19. Construction of explicit Runge-Kutta pairs with stiffness detection
Author(s): Sofroniou M, Spaletta G
Source: MATHEMATICAL AND COMPUTER MODELLING Volume: 40 Issue: 11-12 Pages: 1157-1169 Published: DEC 2004
Times Cited: 1
21. Formation of discontinuities in flux-saturated degenerate parabolic equations
Author(s): Chertock A, Kurganov A, Rosenau P
Source: NONLINEARITY Volume: 16 Issue: 6 Pages: 1875-1898 Published: NOV 2003
Times Cited: 5
22. Telescopic projective methods for parabolic differential equations
Author(s): Gear CW, Kevrekidis IG
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 187 Issue: 1 Pages: 95-109 Published: MAY 1 2003
Times Cited: 25
23. Projective methods for stiff differential equations: Problems with gaps in their eigenvalue spectrum
Author(s): Gear CW, Kevrekidis IG
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 24 Issue: 4 Pages: 1091-1106 Published: 2003
Times Cited: 57
24. Central-upwind schemes for the Saint-Venant system
Author(s): Kurganov A, Levy D
Source: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE Volume: 36 Issue: 3 Pages: 397-425 Published: MAY-JUN 2002
Times Cited: 51
25. A numerical method for the accurate solution of the Fokker-Planck-Landau equation in the nonhomogeneous case
Author(s): Filbet F, Pareschi L
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 179 Issue: 1 Pages: 1-26 Published: JUN 10 2002
Times Cited: 8
26. Fourth order Chebyshev methods with recurrence relation
Author(s): Abdulle A
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 23 Issue: 6 Pages: 2041-2054 Published: MAY 17 2002
Times Cited: 14
27.
This record has been added to your Marked List. Second order Chebyshev methods based on orthogonal polynomials
Author(s): Abdulle A, Medovikov AA
Source: NUMERISCHE MATHEMATIK Volume: 90 Issue: 1 Pages: 1-18 Published: NOV 2001
Times Cited: 20
28. A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems
Author(s): Kurganov A, Petrova G
Source: NUMERISCHE MATHEMATIK Volume: 88 Issue: 4 Pages: 683-729 Published: JUN 2001
Times Cited: 22
29. Explicit time-scale splitting algorithm for stiff problems: Auto-ignition of gaseous mixtures behind a steady shock
Author(s): Valorani M, Goussis DA
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 169 Issue: 1 Pages: 44-79 Published: MAY 1 2001
Times Cited: 29
30. Fast spectral methods for the Fokker-Planck-Landau collision operator
Author(s): Pareschi L, Russo G, Toscani G
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 165 Issue: 1 Pages: 216-236 Published: NOV 20 2000
Times Cited: 9
31. A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations
Author(s): Kurganov A, Levy D
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 22 Issue: 4 Pages: 1461-1488 Published: NOV 8 2000
Times Cited: 72
32. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
Author(s): Kurganov A, Tadmor E
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 160 Issue: 1 Pages: 241-282 Published: MAY 1 2000
Times Cited: 176
33. On roots and error constants of optimal stability polynomials
Author(s): Abdulle A
Source: BIT Volume: 40 Issue: 1 Pages: 177-182 Published: 2000
Times Cited: 5
34. Large-eddy simulation of convective boundary layer using explicit difference schemes
Author(s): Lebedev VI, Loutsenko SV, Lykossov VN
Source: RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING Volume: 15 Issue: 1 Pages: 95-110 Published: 2000
Times Cited: 2
35. S-ROCK: Chebyshev methods for stiff stochastic differential equations
Author(s): Abdulle A, Cirilli S
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 30 Issue: 2 Pages: 997-1014 Published: 2007
Times Cited: 0
36. Asymptotic representation of weighted L-infinity- and L-1-minimal polynomials
Author(s): Kroo A, Peherstorfer F
Source: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Volume: 144 Pages: 241-254 Part: Part 1 Published: JAN 2008
Times Cited: 0
37. Stabilized methods for stiff stochastic systems
Author(s): Abdulle A, Cirili S
Source: COMPTES RENDUS MATHEMATIQUE Volume: 345 Issue: 10 Pages: 593-598 Published: NOV 15 2007
Times Cited: 1
38. On stabilized integration for time-dependent PDEs
Author(s): Sommeijer BP, Verwer JG
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 224 Issue: 1 Pages: 3-16 Published: MAY 20 2007
Times Cited: 1
39. Essentially optimal explicit Runge-Kutta methods with application to hyperbolic-parabolic equations
Author(s): Torrilhon M, Jeltsch R
Source: NUMERISCHE MATHEMATIK Volume: 106 Issue: 2 Pages: 303-334 Published: APR 2007
Times Cited: 0
40. Second-order accurate projective integrators for multiscale problems
Author(s): Lee SL, Gear CW
Source: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 201 Issue: 1 Pages: 258-274 Published: APR 1 2007
Times Cited: 5
41. Two-dimensional bulk microflow simulations based on regularized Grad's 13-moment equations
Author(s): Torrilhon M
Source: MULTISCALE MODELING & SIMULATION Volume: 5 Issue: 3 Pages: 695-728 Published: 2006
Times Cited: 3
42. Numerical methods for transport problems in microdevices
Author(s): Abdulle A, Attinger S
Source: LARGE-SCALE SCIENTIFIC COMPUTING Book Series: LECTURE NOTES IN COMPUTER SCIENCE Volume: 3743 Pages: 67-75 Published: 2006
Times Cited: 0
43. Modeling particle formation at spray drying using population balances
Author(s): Seydel P, Blomer J, Bertling J
Source: DRYING TECHNOLOGY Volume: 24 Issue: 2 Pages: 137-146 Published: 2006
Times Cited: 2
44.
This record has been added to your Marked List. Variable time steps optimization of L-omega-stable Crank-Nicolson method
Author(s): Medovikov AA, Lebedev VI
Source: RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING Volume: 20 Issue: 3 Pages: 283-303 Published: 2005
Times Cited: 1
45. RKC time-stepping for advection-diffusion-reaction problems
Author(s): Verwer JG, Sommeijer BP, Hundsdorfer W
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 201 Issue: 1 Pages: 61-79 Published: NOV 20 2004
Times Cited: 12
46. An implicit-explicit Runge-Kutta-Chebyshev scheme for diffusion-reaction equations
Author(s): Verwer JG, Sommeijer BP
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 25 Issue: 5 Pages: 1824-1835 Published: 2004
Times Cited: 12
47. Soft tissue simulation based on measured data
Author(s): Hauth M, Gross J, Strasser W, et al.
Source: MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION - MICCAI 2003, PT 1 Book Series: LECTURE NOTES IN COMPUTER SCIENCE Volume: 2878 Pages: 262-270 Published: 2003
Times Cited: 0
48. Formation of discontinuities in flux-saturated degenerate parabolic equations
Author(s): Chertock A, Kurganov A, Rosenau P
Source: NONLINEARITY Volume: 16 Issue: 6 Pages: 1875-1898 Published: NOV 2003
Times Cited: 5
49. Competition between protein folding and aggregation with molecular chaperones in crowded solutions: Insight from mesoscopic simulations
Author(s): Kinjo AR, Takada S
Source: BIOPHYSICAL JOURNAL Volume: 85 Issue: 6 Pages: 3521-3531 Published: DEC 2003
Times Cited: 14
50. Finite difference heterogeneous multi-scale method for homogenization problems
Author(s): Abdulle A, Weinan E
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 191 Issue: 1 Pages: 18-39 Published: OCT 10 2003
Times Cited: 19
51. Effects of macromolecular crowding on protein folding and aggregation studied by density functional theory: Dynamics
Author(s): Kinjo AR, Takada S
Source: PHYSICAL REVIEW E Volume: 66 Issue: 5 Article Number: 051902 Published: NOV 2002
Times Cited: 11
52. Central-upwind schemes for the Saint-Venant system
Author(s): Kurganov A, Levy D
Source: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE Volume: 36 Issue: 3 Pages: 397-425 Published: MAY-JUN 2002
Times Cited: 51
53. Fourth order Chebyshev methods with recurrence relation
Author(s): Abdulle A
Source: SIAM JOURNAL ON SCIENTIFIC COMPUTING Volume: 23 Issue: 6 Pages: 2041-2054 Published: MAY 17 2002
Times Cited: 14
54. Method of Submerged Stokeslets for Slip Flow About Ensembles of Particles
Author(s): Zhao S, Povitsky A
Source: JOURNAL OF NANOSCIENCE AND NANOTECHNOLOGY Volume: 8 Issue: 7 Pages: 3790-3801 Published: JUL 2008
Times Cited: 0
55. Unexpected Bipolar Flagellar Arrangements and Long-Range Flows Driven by Bacteria near Solid Boundaries
Author(s): Cisneros LH, Kessler JO, Ortiz R, et al.
Source: PHYSICAL REVIEW LETTERS Volume: 101 Issue: 16 Article Number: 168102 Published: OCT 17 2008
Times Cited: 0
56. Validation of a simple method for representing spheres and slender bodies in an immersed boundary method for Stokes flow on an unbounded domain
Author(s): Bringley TT, Peskin CS
Source: JOURNAL OF COMPUTATIONAL PHYSICS Volume: 227 Issue: 11 Pages: 5397-5425 Published: MAY 10 2008
Times Cited: 0
57. Interaction between arthropod filiform hairs in a fluid environment
Author(s): Cummins B, Gedeon T, Klapper I, et al.
Source: JOURNAL OF THEORETICAL BIOLOGY Volume: 247 Issue: 2 Pages: 266-280 Published: JUL 21 2007
Times Cited: 4
58. Hydrodynamics of bacterial colonies
Author(s): Lega J, Passot T
Source: NONLINEARITY Volume: 20 Issue: 1 Pages: C1-C16 Published: JAN 2007
Times Cited: 3
59. Oseledets, IV 2007-SBORNIK MATHEMATICS Lower bounds for separable approximations of the Hilbert kernel
BOOKS
60. Ernst Hairer Gerhard Wanner Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer Series in Comput. Mathematics, Vol. 14, Springer-Verlag 1991, Second revised edition 1996.
61. Numerical Solution of Time-dependent Advection-diffusion-reaction Equations
By W. H. Hundsdorfer, Jan G. Verwer
62. Numerical Methods and Applications
By Gurii Ivanovich Marchuk
63. Medical Image Computing and Computer-assisted Intervention - MICCAI 2003
By Randy
64. The Immersed Interface Method
By Zhilin Li, Kazufumi Ito