PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1998 | 69 | 1 | 61-74
Tytuł artykułu

On the method of lines for a non-linear heat equation with functional dependence

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a heat equation with a non-linear right-hand side which depends on certain Volterra-type functionals. We study the problem of existence and convergence for the method of lines by means of semi-discrete inverse formulae.
Słowa kluczowe
Rocznik
Tom
69
Numer
1
Strony
61-74
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-14
poprawiono
1997-11-17
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [1] P. Besala, Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26.
  • [2] S. Brzychczy, Chaplygin's method for a system of nonlinear parabolic differential-functional equations, Differentsial'nye Uravneniya 22 (1986), 705-708 (in Russian).
  • [3] L. Byszewski, Monotone iterative method for a system of nonlocal initial-boundary parabolic problems, J. Math. Anal. Appl. 177 (1993), 445-458.
  • [4] Z. Kamont, On the Chaplygin method for partial differential-functional equations of the first order, Ann. Polon. Math. 38 (1980), 27-46.
  • [5] Z. Kamont and H. Leszczyński, Stability of difference equations generated by parabolic differential-functional problems, Rend. Mat. 16 (1996), 265-287.
  • [6] Z. Kamont and H. Leszczyński, Numerical solutions to the Darboux problem with the functional dependence, Georgian Math. J. (1997).
  • [7] Z. Kamont and S. Zacharek, The line method for parabolic differential-functional equations with initial boundary conditions of the Dirichlet type, Atti Sem. Mat. Fis. Univ. Modena 35 (1987), 249-262.
  • [8] M. Krzyżański, Partial Differential Equations of Second Order, PWN, Warszawa, 1971.
  • [9] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Adv. Publ. Program, Pitman, Boston, 1985.
  • [10] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967 (in Russian); English transl.: Transl. Math. Monographs 23, Amer. Math. Soc., Providence, R.I., 1968.
  • [11] H. Leszczyński, Convergence of one-step difference methods for nonlinear parabolic differential-functional systems with initial boundary conditions of Dirichlet type, Comment. Math. Prace Mat. 30 (1991), 357-375.
  • [12] H. Leszczyński, A new existence result for a non-linear heat equation with functional dependence, Comment. Math. Prace Mat. 37 (1997), 155-181.
  • [13] H. Leszczyński, General finite difference approximation to the Cauchy problem for non-linear parabolic differential-functional equations, Ann. Polon. Math. 53 (1991), 15-28.
  • [14] H. Leszczyński, Convergence results for unbounded solutions of first order non-linear differential-functional equations, Ann. Polon. Math. 64 (1996), 1-16.
  • [15] H. Leszczyński, Discrete approximations to the Cauchy problem for hyperbolic differential-functional systems in the Schauder canonic form, Zh. Vychisl. Mat. Mat. Fiz. 34 (1994), 185-200 (in Russian); English transl.: Comput. Math. Math. Phys. 34 (1994), 151-164.
  • [16] 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. B (7) 1 (1987), 99-109.
  • [17] L. F. Shampine, ODE solvers and the method of lines, Numer. Methods Partial Differential Equations 10 (1994), 739-755.
  • [18] A. Voigt, Line method approximation to the Cauchy problem for nonlinear differential equations, Numer. Math. 23 (1974), 23-36.
  • [19] A. Voigt, The method of lines for nonlinear parabolic differential equations with mixed derivatives, Numer. Math. 32 (1979), 197-207.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z1p61bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.