A boundary method of Trefftz type with approximate trial functions

This paper presents a new numerical technique which belongs to the group of the Trefftz type methods. It differs from the other boundary techniques by the use of approximate solutions of the corresponding partial differential equations (PDE) as trial functions. This permits to extend the field of application of this boundary method to the problem where one cannot find an appropriate set of exact solutions. In particular, the application of the method presented to a general PDE of the elliptic type is considered in the paper. The method has also been found to work well for certain boundary value and initial value problems including PDEs of the fourth order and equations of the nonstationary heat transfer with moving boundaries. (C) 2002 Elsevier Science Ltd. All rights reserved.