Explicit difference schemes for nonlinear differential functional parabolic equations with mixed derivatives-convergence analysis

• Autorzy: Poliński A.
• Języki publikacji: EN

Abstrakty

EN

We study the initial-value problem for parabolic equations with mixed partial derivatives and constant coefficients, and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyse convergence of explicit finite difference schemes by means of discrete fundamental solutions.

Słowa kluczowe

EN

finite differences; stability; parabolic; nonlocal

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2005
• Tom: Vol. 45, [Z] 2
• Strony: 205--217
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Poliński A.

• Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Poland,

Bibliografia

• [1] P. Besala, Finite difference approximation to the Cauchy problem for nonlinear parabolic differential equations, Ann. Polon. Math. 46 (1985), 19-26.
• [2] Z. Kamont, Hyperbolic Functional Differental Inequalities and Applications, Kluver Academic Publishers, Dordrecht Boston London 1999.
• [3] Z. Kamont and H. Leszczyński, Stability of difference equations generated by parabolic differential-functional problems, Rend. Mat. Appl. 16 (1996), 265-287.
• [4] D. Kleitman, On a lemma of Littlewood and Offord on the distribution of certain sums, Math. Zeitschrift 90 (1965), 251-259.
• [5] H. Leszczyński, Finite difference schemes for a non-linear heat equation with functional dependence, ZAMM 79 (1999), 53-64.
• [6] M. Malec, Sur une méthode des différences finies pour une équation non linéaire intégro-différentielle a argument retardé, (French) Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 501-512.
• [7] M. Malec, C. Ma̧czka and W. Voigt, Weak difference-functional inequalities and their application to the difference analogue of nonlinear parabolic differential-functional equations, Beiträge Numer. Math. 11 (1983), 69-79.