Stiff ODE solvers: A review of current and coming attractions

Journal of Computational Physics

Volumn 70, Issue 1, 1987, Pages 1-62

  Byrne, George D ^a   Hindmarsh, Alan C ^b  

^a EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006178478     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/0021-9991(87)90001-5     Document Type: Review

References (144)

1. Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
2. Correction in the dominant space: a numerical technique for a certain class of stiff initial value problems
3. Software for Time-Dependent Problems
4. A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas
5. The order of numerical methods for ordinary differential equations
6. General Linear Methods: Prospects as Stiff Solvers
7. The ODE Solver EPISODE, Its Variants and Their Use
8. A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
9. Pseudo-Runge-Kutta Methods Involving Two Points
10. The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVPsfor ODEs
11. Simulation of Chemical Kinetics Transport in the Stratosphere
12. A simplified Galerkin method for hyperbolic equations
13. Solution of Large, Stiff Initial Value Problems-The state of the Art
14. Integration of Stiff Equations
15. Global Error Estimation in ODE-Solvers
16. On the Control of Global Error in Stiff Initial Value Problems
17. On the Local and Global Errors of One-Leg Methods
18. LARKIN-A Software Package for the Numerical Simulation of Large Systems Arising in Chemical Reaction Kinetics
19. The Numerical Solution of a Composition Model in Petroleum Reservoir Engineering
20. Yale sparse matrix package I: The symmetric codes
21. Modular Simulation of Large Stiff Systems
22. Comparing Numerical Methods for the Solution of Stiff Systems of ODEs Arising in Chemistry
23. The Automatic Integration of Stiff Ordinary Differential Equations
24. Simultaneous Numerical Solution of Differential-Algebraic Equations
25. Runge-Kutta Starters for Multistep Methods
26. Lawrence Livermore Laboratory Report No. UCRL-75373
27. A Mathematical Model of Thermal Oil Recovery in Linear Systems
28. The Sparse Tableau Approach to Network Analysis and Design
29. Lawrence Livermore Laboratory Report No. UCID-30001, Rev. 3
30. A Collection of Software for Ordinary Differential Equations
31. LSODE and LSODI, two new initial value ordinary differnetial equation solvers
32. ODE Solvers for Use with the Method of Lines
33. ODEPACK, a Systematized Collection of ODE Solvers
34. Applications of EPISODE: An Experimental Package for the Integration of Systems of Ordinary Differential Equations
35. Discrete Galerkin and related one-step methods for ordinary differential equations
36. PECE Algorithms for the Solution of Stiff Systems of Ordinary Differential Equations
37. DISPL2: A Software Package for Solving One and T'wo Spatially Dimonsioned Convection-Diffusion Kinetics Nonlinear PDEs
38. A Stiff System Package Based on the Implicit Midpoint Method
39. High-Order A-Stable Averaging Algorithms for Stiff Differential Systems
40. Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
41. The Numerical Method of Lines for the Solution of Nonlinear Partial Differential Equations
42. Minimal error constant numerical differentiation (N.D.) formulas
43. Differential/Algebraic Equations are not ODE’s
44. A Description of DASSL: A Differential-Algebraic System Solver
45. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
46. Estimating the Accuracy of Numerical Solutions to Ordinary Differential Equations
47. The Solution of a Set of Reaction Rate Equations
48. Global Error Estimates for Solutions to Stiff Systems of Ordinary Differential Equations
49. A Runge-Kutta for all Seasons
50. An Efficient Algorithm Using Backward Time-Scaled Differences for Solving Stiff Differential-Algebraic Systems
51. Bell Laboratories Computer Science Technical Report No. 53
52. A Systematized Collection of Codes for Solving Two-Point Boundary-Value Problems
53. A User’s View of Solving Stiff Ordinary Differential Equations
54. GEARS: A Package for the Solution of Sparse, Stiff Ordinary Differential Equations
55. Software for Nonlinear Partial Differential Equations
56. Analysis of descriptor systems using numerical algorithms
57. Blended Linear Multistep Methods
58. Global Error Estimation in ODE-Solvers
59. Generalized finite-difference schemes
60. A stiffly stable integration process using cyclic composite methods
61. Algorithm 534: STINT: STiff (differential equations) INTegrator [D2]: STINT: STiff (differential equations) INTegrator [D2]
62. Automatic ODE Software for Use in an Industrial Environment
63. Cosiderations in Designing a Cyclic Method Stiff ODE Solver
64. A New Class of Cyclic Multistep Formulae for Stiff Systems
65. One-Leg Formulas for Stiff Ordinary Differential Equations