On the Chaplygin method for the Darboux problem

• Autorzy: Jaruszewska-Walczak D.
• Języki publikacji: EN

Abstrakty

EN

In the paper we deal with the Darboux problem for hyperbolic functional differntial equations. We give the sufficient conditions for the existence of the sequence {z^(m)} such that if z is a classical solution of the original problem then {z^(m)} is uniformly convergent to z. The convergence that we get is of the Newton type.

Słowa kluczowe

EN

functional differential equation; Newton method; analytical approximations

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 1
• Strony: 11--21
• Opis fizyczny: bibliogr. 9 poz.

Twórcy

autor

Jaruszewska-Walczak D.

• University of Gdańsk Institute of mathematics, Wit Stwosz Str. 57, 80-952 Gdańsk, Poland,

Bibliografia

• [1] S. Brzychczy, Chaplygin's method for a system of nonlinear parabolic differential-functional equations (Russian), Diff. Urav. 22 (1986), 705-708.
• [2] S. A. Chaplygin, Selected Works on Mechanics and Mathematics (Russian), Moscow 1954.
• [3] T. Człapinski, Iterative methods for the Darboux problem for partial differential-functional equations, J. Inequal. Appl. 4(2) (1999), 141-161.
• [4] Z. Kamont, On the Chaplygin method for partial differential-functional equations of the first order, Ann. Polon. Math. 38 (1980), 313-324.
• [5] W. I. Krylov, W. W. Bobkov, P. I. Monastyrnyi, Numerical Methods (Russian), vol. 1, Moscow 1976.
• [6] W. Mlak, E. Schechter, On the Chaplygin method for partial differential equations of the first order, Ann. Polon. Math. 22 (1969), 1-18.
• [7] J. Szarski, Differential Inequalities, Warszawa 1967.
• [8] G. Vidossich, Chaplygin's method is Newton's method, J. Math. Anal. Appl. 66(1) (1978), 188-206.
• [9] P. K. Zeragia, Chaplygin's method for nonlinear hyperbolic differential equations with boundary conditions, (Georgian), Trudy Tbil. Gos. Univ. 100 (1965), 145-154.