Difference methods for the Darboux problem for functional partial differential equations

Tomasz Człapiński

Annales Polonici Mathematici (1999)

  • Volume: 71, Issue: 2, page 171-193
  • ISSN: 0066-2216

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Tomasz Człapiński. "Difference methods for the Darboux problem for functional partial differential equations." Annales Polonici Mathematici 71.2 (1999): 171-193. <http://eudml.org/doc/262534>.

@article{TomaszCzłapiński1999,
abstract = {},
author = {Tomasz Człapiński},
journal = {Annales Polonici Mathematici},
keywords = {functional differential equation; Darboux problem; classical; comparative method; two convergence theorems for implicit and explicit schemes},
language = {eng},
number = {2},
pages = {171-193},
title = {Difference methods for the Darboux problem for functional partial differential equations},
url = {http://eudml.org/doc/262534},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Tomasz Człapiński
TI - Difference methods for the Darboux problem for functional partial differential equations
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 2
SP - 171
EP - 193
AB -
LA - eng
KW - functional differential equation; Darboux problem; classical; comparative method; two convergence theorems for implicit and explicit schemes
UR - http://eudml.org/doc/262534
ER -

References

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  1. [1] P. Brandi, Z. Kamont and A. Salvadori, Approximate solutions of mixed problems for first order partial differential-functional equations, Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 277-302. Zbl0737.35134
  2. [2] T. Człapiński, Existence of solutions of the Darboux problem for partial differen- tial-functional equations with infinite delay in a Banach space, Comment. Math. 35 (1995), 111-122. Zbl0859.35131
  3. [3] Z. Denkowski and A. Pelczar, On the existence and uniqueness of solutions of some partial differential functional equations, Ann. Polon. Math. 35 (1978), 261-304. 
  4. [4] Z. Kamont, Finite difference approximations for first-order partial differential-functional equations, Ukrain. Math. J. 46 (1994), 265-287. 
  5. [5] Z. Kamont and M. Kwapisz, On the Cauchy problem for differential-delay equations in a Banach space, Math. Nachr. 74 (1976), 173-190. Zbl0288.34069
  6. [6] Z. Kamont and M. Kwapisz, On non-linear Volterra integral-functional equations in several variables, Ann. Polon. Math. 40 (1981), 1-29. Zbl0486.45011
  7. [7] Z. Kamont and H. Leszczyński, Stability of difference equations generated by parabolic differential-functional problems, Rend. Mat. 16 (1996), 265-287. Zbl0859.65094
  8. [8] Z. Kamont and H. Leszczyński, Numerical solutions to the Darboux problem with the functional dependence, Georgian Math. J. 5 (1998), 71-90. Zbl0955.65076
  9. [9] H. Leszczyński, Convergence of one-step difference methods for nonlinear para- bolic differential-functional systems with initial-boundary conditions of the Dirichlet type, Comment. Math. 30 (1990), 357-375. 
  10. [10] H. Leszczyński, Convergence of difference analogues to the Darboux problem with functional dependence, Bull. Belgian Math. Soc. 5 (1998), 39-57. Zbl0920.35163
  11. [11] M. Malec, C. Mączka and W. Voigt, Weak difference-functional inequalities and their applications to the difference analogue of non-linear parabolic differential-functional equations, Beiträge Numer. Math. 11 (1983), 69-79. Zbl0526.34056
  12. [12] M. Malec and M. Rosati, Weak monotonicity for non linear systems of functional-finite difference inequalities of parabolic type, Rend. Mat. 3 (1983), 157-170. Zbl0557.39006
  13. [13] M. Malec et A. Schiaffino, Méthode aux différence finies pour une équation non-linéaire différentielle fonctionnelle du type parabolique avec une condition initiale de Cauchy, Boll. Un. Mat. Ital. 7B (1987), 99-109. Zbl0617.65083
  14. [14] A. Pelczar, Some functional-differential equations, Dissertationes Math. 100 (1973). 
  15. [15] T. Ważewski, Sur une extension du procédé de I. Jungermann pour établir la convergence des approximations successives au cas des équations différentielles ordinaires, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 43-46. Zbl0091.28801
  16. [16] M. Zennaro, Delay differential equations: theory and numerics, in: Theory and Numerics of Ordinary and Partial Differential Equations, Clarendon Press, Oxford, 1995, 291-333. Zbl0847.34072

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