A non-standard explicit integration scheme for initial-value problems

Applied Mathematics and Computation

Volumn 189, Issue 1, 2007, Pages 710-718

  Ramos, Higinio ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

Non standard algorithm; Singular initial value problems; Singularly perturbed initial value problems; Stiff initial value problems

Indexed keywords

ALGORITHMS; INTEGRATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

NON-STANDARD ALGORITHM; SINGULAR INITIAL VALUE PROBLEMS; SINGULARLY PERTURBED INITIAL VALUE PROBLEMS; STIFF INITIAL-VALUE PROBLEMS;

INITIAL VALUE PROBLEMS;

EID: 34248388581     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.11.134     Document Type: Article

References (16)

1. O'Malley R.E. Singular Perturbation Methods for Ordinary Differential Equations (1991), Springer-Verlag, New York
2. Roos H.G., Stynes M., and Tobiska L. Numerical Methods for Singularly Perturbed Differential Equations (1996), Springer, Berlin
3. Roberts S.M. A boundary-value technique for singular perturbation problems. J. Math. Anal. Appl. 79 (1982) 489-508
4. Natesan S., Vigo-Aguiar J., and Ramanujam N. A numerical algorithm for singular perturbation problems exhibiting weak boundary layers. Comput. Math. Appl. 45 (2003) 469-479
5. van Niekerk F.D. Nonlinear one-step methods for initial value problems. Comput. Math. Appl. 13 (1987) 367-371
6. Lambert J.D. Numerical Methods for Ordinary Differential Systems (1991), John Wiley, England
7. Fatunla S.O. Numerical Methods for IVPs in ODEs (1988), Academic Press Inc., London
8. Fatunla S.O. Nonlinear multistep methods for initial value problems. Comput. Math. Appl. 8 3 (1982) 231-239
9. Fatunla S.O. Numerical treatment of singular initial value problems. Comput. Math. Appl. 12B 56 (1986) 1109-1115
10. van Niekerk F.D. Rational one-step methods for initial value problems. Comput. Math. Appl. 16 12 (1987) 1035-1039
11. Abelman S., and Eyre D. A numerical study of multistep methods based on continued fractions. Comput. Math. Appl. 20 8 (1990) 51-60
12. Odekunle M.R., Oye N.D., Adee s.O., and Ademiluyi R.A. A class of inverse Runge-Kutta schemes for the numerical integration of singular problems. Appl. Math. Comput. 158 (2004) 149-158
13. Hairer E., and Wanner G. Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems (1996), Springer, Berlin
14. Ahmad R.R., Yaacob N., and Mohd Murid A.H. Explicit methods in solving stiff ordinary differential equations. Int. J. Comput. Math. 81 (2004) 1407-1415
15. Wu X.-Y., and Xia J.-L. Two low accuracy methods for stiff systems. Appl. Math. Comput. 123 (2001) 141-153
16. Ramos J.I. Linearization techniques for singularly-perturbed initial-value problems of ordinary differential equations. Appl. Math. Comput. 163 (2005) 1143-1163