# Convergence results for unbounded solutions of first order non-linear differential-functional equations

Annales Polonici Mathematici (1996)

- Volume: 64, Issue: 1, page 1-16
- ISSN: 0066-2216

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topHenryk Leszczyński. "Convergence results for unbounded solutions of first order non-linear differential-functional equations." Annales Polonici Mathematici 64.1 (1996): 1-16. <http://eudml.org/doc/269997>.

@article{HenrykLeszczyński1996,

abstract = {We consider the Cauchy problem in an unbounded region for equations of the type either $D_\{t\}z(t,x) = f(t,x,z(t,x),z_\{(t,x)\},D_\{x\}z(t,x))$ or $D_\{t\}z(t,x)= f(t,x,z(t,x),z,D_\{x\}z(t,x))$. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.},

author = {Henryk Leszczyński},

journal = {Annales Polonici Mathematici},

keywords = {error estimates; recurrence inequalities; difference scheme; Cauchy problem},

language = {eng},

number = {1},

pages = {1-16},

title = {Convergence results for unbounded solutions of first order non-linear differential-functional equations},

url = {http://eudml.org/doc/269997},

volume = {64},

year = {1996},

}

TY - JOUR

AU - Henryk Leszczyński

TI - Convergence results for unbounded solutions of first order non-linear differential-functional equations

JO - Annales Polonici Mathematici

PY - 1996

VL - 64

IS - 1

SP - 1

EP - 16

AB - We consider the Cauchy problem in an unbounded region for equations of the type either $D_{t}z(t,x) = f(t,x,z(t,x),z_{(t,x)},D_{x}z(t,x))$ or $D_{t}z(t,x)= f(t,x,z(t,x),z,D_{x}z(t,x))$. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.

LA - eng

KW - error estimates; recurrence inequalities; difference scheme; Cauchy problem

UR - http://eudml.org/doc/269997

ER -

## References

top- [1] P. Besala, On solutions of first order partial differential equations defined in an unbounded zone, Bull. Acad. Polon. Sci. 12 (1964), 95-99. Zbl0151.14304
- [2] P. Besala, Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26. Zbl0601.65073
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- [4] M. Krzyżański, Partial Differential Equations of Second Order, PWN, Warszawa, 1971.
- [5] H. Leszczyński, General finite difference approximation to the Cauchy problem for non-linear parabolic differential-functional equations, Ann. Polon. Math. 53 (1991), 15-28. Zbl0731.65079
- [6] H. Leszczyński, Uniqueness results for unbounded solutions of first order non-linear differential-functional equations, Acta Math. Hungar. 64 (1994), 75-92. Zbl0804.35137
- [7] M. Malec et A. Schiaffino, Méthode aux différences finies pour une équation non-linéaire différentielle fonctionnelle du type parabolique avec une condition initiale de Cauchy, Boll. Un. Mat. Ital. (7) 1-B (1987), 99-109. Zbl0617.65083
- [8] K. Prządka, Difference methods for non-linear partial differential functional equations of the first order, Math. Nachr. 138 (1988), 105-123. Zbl0668.65093
- [9] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.

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