TY  - JOUR
ID  - JaruszewskaWalczak2004
LB  - JaruszewskaWalczak2004
AU  - Jaruszewska-Walczak, Danuta
TI  - Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid
ST  - Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2004
VL  - 24
IS  - 1
SP  - 85
EP  - 96
DO  - http://dx.doi.org/10.7494/OpMath.2004.24.1.85
UR  - http://dx.doi.org/10.7494/OpMath.2004.24.1.85
AB  - We consider the Cauchy problem for infinite system of differential functional equations \[\partial_tz_k(t,x)=f_k(t,x,z,\partial_xz_k(t,x)),\;k\in\mathbf{N}.\] In the paper we consider a general class of difference methods for this problem. We prove the convergence of methods under the assumptions that given functions satisfy the nonlinear estimates of the Perron type with respect to functional variables. The proof is based on functional difference inequalities. We constructed the Euler method as an example of difference method.
KW  - initial problems
KW  - infinite systems of differential functional equations
KW  - difference functional inequalities
KW  - nonlinear estimates of the Perron type
SN  - 1232-9274
ER  -