On an accurate third order implicit-explicit Runge-Kutta method for stiff problems

Applied Numerical Mathematics

Volumn 59, Issue 7, 2009, Pages 1515-1528

  Boscarino, Sebastiano ^a  

^a UNIVERSITY OF CATANIA   (Italy)

Author keywords

Order reduction; Runge Kutta methods; Stiff problems

Indexed keywords

IMPLICIT-EXPLICIT; IMPLICIT-EXPLICIT RUNGE-KUTTA METHODS; ORDER REDUCTION; RUNGE-KUTTA; STIFF PROBLEMS; STIFF TERMS; TEMPORAL ORDERS; THIRD ORDERS;

RUNGE KUTTA METHODS;

EID: 63249124455     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2008.10.003     Document Type: Article

References (25)

1. Ascher U., Ruuth S., and Spiteri R.J. Implicit-explicit Runge-Kutta methods for time dependent partial differential equations. Appl. Numer. Math. 25 (1997) 151-167
2. Ascher U., Ruuth S., and Wetton B.T.R. Implicit-explicit methods for time dependent PDE's. Appl. Numer. Math. 32 (1995) 797-823
3. Blom J.G., Hundsdorfer W., and Verwer J.G. An implicit-explicit approach for atmospheric transport-chemistry problems. Workshop on the Method of Lines for Time-Dependent Problems. Lexington, KY, 1995. Appl. Numer. Math. 20 1-2 (1996) 191-209
4. Boscarino S. Error analysis of IMEX Runge-Kutta methods derided from differential algebraic systems. SIAM J. Numer. Anal. 45 4 (2007) 1600-1621
5. S. Boscarino, On the uniform accuracy of implicit-explicit Runge-Kutta methods, Ph.D. Thesis in Mathematics for the Technology, Department of Mathematics and Computer Science, University of Catania, Italy, 2005
6. Calvo M.P., de Frutos J., and Novo J. Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations. Appl. Numer. Math. 37 (2001) 535-549
7. Carpenter M.H., and Kennedy C.A. Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44 1-2 (2003) 139-181
8. Cole J.D. On a quasi-linear parabolic equation occurring in aerodynamics. Quart. Appl. Math. 9 (1978) 225
9. Frank J., Hundsdorfer W., and Verwer J.G. On the stability of implicit-explicit linear multistep methods. Appl. Numer. Math. 25 2-3 (1997) 193-205 Special issue on time integration
10. Garcia-Celayeta B., Higueras I., and Roldan T. Contractivity/monotonicity for additive Runge-Kutta methods: Inner product norms. Appl. Numer. Math. 56 (2006) 862-878
11. E. Hairer, Order conditions for numerical methods for partitioned ordinary differential equations, Numer. Math. 36, 431-445
12. Hairer E., Lubich Ch., and Roche M. Error of Runge-Kutta methods for stiff problems via differential algebraic equations. BIT 28 3 (1988) 678-700
13. Hairer E., Lubich Ch., and Roche M. The Numerical Solution of Differential Algebraic Systems by Runge-Kutta Methods. Lecture Notes in Mathematics vol. 1409 (1989), Springer-Verlag
14. Hairer E., Lubich Ch., and Wanner G. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics vol. 31 (2002), Springer-Verlag, Berlin
15. Hairer E., Nørsett S.P., and Wanner G. Solving Ordinary Differential Equation I: Non Stiff Problems. Springer Series in Computational Mathematics vol. 8 (1987), Springer-Verlag second revised edition, 1993
16. Hairer E., and Wanner G. Solving Ordinary Differential Equation II: Stiff and Differential Algebraic Problems. Springer Series in Computational Mathematics vol. 14 (1991), Springer-Verlag second revised edition, 1996
17. Hairer E., and Wanner G. On the Butcher group and general multi-value methods. Computing 13 1 (1974) 1-15
18. Hundsdorfer W., and Jaffré J. Implicit-explicit time stepping with spatial discontinuous finite elements. Appl. Numer. Math. 45 2-3 (2003) 231-254
19. Liotta S.F., Romano V., and Russo G. Central schemes for balance laws of relaxation type. SIAM J. Numer. Anal. 38 (2000) 1337-1356
20. Pareschi L., and Russo G. Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations. Recent Trends in Numerical Analysis. Adv. Theory Comput. Math. vol. 3 (2001), Nova Sci. Publ., Huntington, NY 269-288
21. O'Malley R.M. Introduction to Singular Perturbations (1974), Academic Press, New York
22. Pareschi L., and Russo G. High order asymptotically strong-stability-preserving methods for hyperbolic systems with stiff relaxation. Hyperbolic Problems: Theory, Numerics, Applications (2003), Springer, Berlin 241-251
23. Pareschi L., and Russo G. Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxations. J. Sci. Comput. 25 1 (October, 2005) 129-155
24. Shu C.W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Advanced Numerical Approximation of Nonlinear Hyperbolic Equation. Lecture Notes in Mathematics vol. 1967 (2000), Springer, New York
25. Tikhonov A.N., Vasl'eva A.B., and Sveshnikov A.G. Differential Equations (1985), Springer-Verlag Translated from the Russian by A.B. Sossinskij