<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">R. Ciarski</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NUMERICAL METHODS FOR QUASILINEAR PARABOLIC DIFFERENTIAL FUNCTIONAL EQUATIONS WITH NEUMANN INITIAL BOUNDARY CONDITIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">Numerical Methods for Quasilinear Parabolic Equations</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35R10</style></keyword><keyword><style  face="normal" font="default" size="100%">65M12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2006</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/10/3/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">10</style></volume><pages><style face="normal" font="default" size="100%">329</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type and coefficients satisfying Perron estimates. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on local properties of the coefficients of the differential equation. A numerical example is given.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">313</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Z. Kamont</style></author><author><style face="normal" font="default" size="100%">A. Nadolski</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS AND APPLICATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">Stability of Functional Difference Equations  </style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35R10</style></keyword><keyword><style  face="normal" font="default" size="100%">65M12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2005</style></year><pub-dates><date><style  face="normal" font="default" size="100%">04/2005</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/9/2/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">246</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type with an unknown function of one variable is presented. The error is estimated by a solution of an initial problem for nonlinear difference equation. This general result is applied to the investigation of the stability of the generalized Lax method for first order partial functional differential equations. Classical solutions of nonlinear problems are approximated in the paper by solutions of suitable quasilinear systems of difference equations. This new approach to the numerical solving of nonlinear equations is generated by a quasilinearization technique. Numerical examples are presented.&lt;/p&gt;

&lt;p class=&quot;rtejustify&quot;&gt;&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">227</style></section></record></records></xml>