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

• Autorzy: Henryk Leszczyński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

error estimates; recurrence inequalities; difference scheme

Kategorie tematyczne

• 35B35: Stability
• 35A35: Theoretical approximation to solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 1
• Strony: 1-16

Daty

wydano

1996

otrzymano

1992-08-28

poprawiono

1996-02-09

Twórcy

autor

Henryk Leszczyński

• Institute of Mathematics, University of Gdańsk, 57 Wita Stwosza St., 80-952 Gdańsk, Poland

Bibliografia

• [1] P. Besala, On solutions of first order partial differential equations defined in an unbounded zone, Bull. Acad. Polon. Sci. 12 (1964), 95-99.
• [2] P. Besala, Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26.
• [3] Z. Kamont, On the Cauchy problem for system of first order partial differential equations, Serdica 5 (1979), 327-339.
• [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.
• [6] H. Leszczyński, Uniqueness results for unbounded solutions of first order non-linear differential-functional equations, Acta Math. Hungar. 64 (1994), 75-92.
• [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.
• [8] K. Prządka, Difference methods for non-linear partial differential functional equations of the first order, Math. Nachr. 138 (1988), 105-123.
• [9] J. Szarski, Differential Inequalities, PWN, Warszawa, 1967.