Abstract
Abstract In this article we present different types of Trefftz functions for stationary and non-stationary linear differential equations. The Trefftz methods are then defined and briefly described. One of them, namely the LSM applied to the region divided on finite elements, is discussed. Examples of the T-functions usage in solving inverse problems and smoothing inaccurate input data are presented. Moreover, some remarks concerning nonlinear non-stationary problem of heat conduction is briefly discussed and some open problems are formulated.
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