Waveform relaxation methods for functional differential systems of neutral type

Journal of Mathematical Analysis and Applications

Volumn 207, Issue 1, 1997, Pages 255-285

  Jackiewicz, Z ^a   Kwapisz, M ^b   Lo, E ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF GDA SK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FUNCTIONS; ITERATIVE METHODS; NUMERICAL ANALYSIS; RELAXATION PROCESSES; WAVEFORM ANALYSIS;

CONTINUOUS TIME ITERATIONS; DISCRETE VARIABLE METHODS; FUNCTIONAL DIFFERENTIAL SYSTEMS; WAVEFORM RELAXATION;

DIFFERENTIAL EQUATIONS;

EID: 0031081858     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5308     Document Type: Article

References (36)

1. 1. H. T. Banks and F. Kappel, Spline approximations for functional differential equations, J. Differential Equations 34 (1979), 496-522.
2. 2. A. Bellen and M. Zennaro, The use of Runge-Kutta formulae in waveform relaxation methods, Appl. Numer. Math. 11 (1993), 95-114.
3. 3. A. Bellen, Z. Jackiewicz, and M. Zennaro, Stability analysis of time-point relaxation Heun method, report "Progretto Finalizzato Sistemi Informatici e Calcolo Parallele" No. 1/30, 1990.
4. 4. A. Bellen, Z. Jackiewicz, and M. Zennaro, Time-point relaxation Runge-Kutta methods for ordinary differential equations, J. Comput. Appl. Math. 45 (1993), 121-137.
5. 5. A. Bellen, Z. Jackiewicz, and M. Zennaro, Contractivity of waveform relaxation Runge-Kutta methods for dissipative systems in the maximum norm, SIAM J. Numer. Anal. 31 (1994), 499-523.
6. 6. M. Bjørhus, On dynamic iteration for delay differential equations, BIT 34 (1994), 325-336.
7. 7. Z. Jackiewicz, The numerical solution of Volterra functional differential equations of neutral type, SIAM J. Numer. Anal. 18 (1981), 615-626.
8. 8. Z. Jackiewicz, Adams methods for neutral functional differential equations, Numer. Math. 39 (1982), 221-230.
9. 9. Z. Jackiewicz, One step methods of any order for neutral functional differential equations, SIAM J. Numer. Anal. 21 (1984), 486-511.
10. 10. Z. Jackiewicz, Quasilinear multistep methods and variable step predictor-corrector methods for neutral functional differential equations, SIAM J. Numer. Anal. 23 (1986), 423-452.
11. 11. Z. Jackiewicz, Variable step variable order algorithm for the numerical solution of functional-differential equations, Appl. Numer. Math. 3 (1987), 317-329.
12. 12. Z. Jackiewicz, Stability analysis of time-point relaxation Runge-Kutta methods with respect to tridiagonal systems of differential equations, Appl. Numer. Math. 11 (1993), 189-209.
13. 13. Z. Jackiewicz and E. Lo, The numerical solution of neutral functional-differential equations by Adams predictor-corrector methods, Appl. Numer. Math. 8 (1991), 477-491.
14. 14. Z. Jackiewicz and E. Lo, The numerical integration of neutral functional-differential equations by fully implicit one-step methods, Z. Angew. Math. Mech. 75 (1995), 207-221.
15. 15. F. L. Juang, "Waveform Methods for Ordinary Differential Equations," Report No. UIUCDCS-R-90-1563, Department of Mathematics, University of Illinois at Urbana-Champaign, 1990.
16. 16. Z. Kamont and M. Kwapisz, On the Cauchy problem for differential delay equations in a Banach space, Math. Nachr. 26 (1981), 97-110.
17. 17. Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Academic Press, San Diego, 1993.
18. 18. E. Lelarasmee, "The Waveform Relaxation Method for the Time Domain Analysis of Large Scale Nonlinear Dynamical Systems," Ph.D. Thesis, University of California, Berkeley, CA, 1982.
19. 19. E. Lelarasmee, A. Ruehli, and A. Sangiovanni-Vincentelli, The waveform relaxation methods for time domain analysis of large scaled integrated circuits, IEEE Trans. CAD IC Systems 1 (1982), 131-145.
20. 20. I. Lie and R. Skålin, Relaxation based integration by Runge-Kutta methods and its application to the moving finite element method, manuscript.
21. 21. E. Lo, "Numerical Solution of Neutral Functional Differential Equations," Ph.D. Thesis, Arizona State University, Tempe, AZ, 1993.
22. 22. E. Lo and Z. Jackiewicz, The algorithm SNDDELM for the numerical solution of systems of neutral delay differential equations, in "Delay Differential Equations with Applications in Population Dynamics" (Y. Kuang, Ed.), Appendix, Academic Press, San Diego, 1993.
23. 23. D. I. Martinjuk, "Lectures on Qualitative Theory of Difference Equations," Naukova Dumka, Kiev, 1972. [In Russian]
24. 24. V. Miekkala and O. Nevanlinna, Convergence of dynamics iteration methods for initial value problems, SIAM J. Sci. Statist. Comput. 8 (1987), 459-482.
25. 25. U. Miekkala and O. Nevanlinna, Sets of convergence and stability regions, BIT 27 (1987), 557-584.
26. 26. O. Nevanlinna, Remarks on Picard-Lindelöf iteration, Part I, BIT 29 (1989), 328-346.
27. 27. O. Nevanlinna, Remarks on Picard-Lindelöf iteration, Part II, BIT 29 (1989), 535-562.
28. 28. O. Nevanlinna, Linear acceleration of Picard-Lindelöf iteration, Numer. Math. 57 (1990), 147-156.
29. 29. K. W. Neves, Automatic integration of functional differential equations: An approach, ACM Trans. Math. Software 1 (1975), 357-368.
30. 30. K. W. Neves, Control of interpolatory error in retarded differential equations, ACM Trans. Math. Software 7 (1981), 421-444.
31. 31. L. Peterson and S. Mattison, Partitioning tradeoffs for waveform relaxation in transient analysis circuit simulation, in "Proc. of the Fifth Distributed Memory Computing Conference" (D. Walker and Q. Stout, Eds.), pp. 612-621, IEEE, Los Alamitos, CA, 1990.
32. 32. R. Skeel, Waveform iteration and the shifted Picard splitting, SIAM J. Sci. Statist. Comput. 10 (1989), 756-776.
33. 33. S. Vanderwalle, "The Parallel Solution of Parabolic Partial Differential Equations by Multi-grid Waveform Relaxation Methods," Ph.D. Thesis, Katholieke Universiteit Leuven, Leuven, 1992.
34. 34. J. White and A. Sangiovanni-Vincentelli, "Relaxation Techniques for the Simulation of VLSI Circuits," Kluwer Academic, Boston, 1987.
35. 35. J. White, A. Sangiovanni-Vincentelli, F. Odeh, and A. Ruehli, Waveform relaxation: Theory and practice, Trans. Soc. Comput. Simulation 2 (1985), 95-133.
36. 36. E. Xia, "Parallel Waveform-Relaxation Newton for Circuit Simulation," Report No. 772, Center for Supercomputing Research and Development, University of Illinois, 1988.