Opuscula Math. 24, no. 1 (2004), 85-96

 
Opuscula Mathematica

Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid

Danuta Jaruszewska-Walczak

Abstract. 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.

Keywords: initial problems, infinite systems of differential functional equations, difference functional inequalities, nonlinear estimates of the Perron type.

Mathematics Subject Classification: 65M10, 65M15, 35R10.

Full text (pdf)

Opuscula Mathematica - cover

Cite this article as:
Danuta Jaruszewska-Walczak, Difference methods for infinite systems of hyperbolic functional differential equations on the Haar pyramid, Opuscula Math. 24, no. 1 (2004), 85-96

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.