SUMMARYThe Boundary Element Method is a very e ective method for solving linear di erential equations. To use it also in the consideration of non-linear problems some di erent procedures were developed, among them the dual reciprocity method and the particular integral method. Both procedures use interpolation conditions for the approximation with radial basis functions. In this paper a method is presented which avoids problems connected with interpolation by means of quasi-interpolation. It is possible to solve di erential equations of the kind m u = p(u) approximately; the application to two non-linear problems of plate theory yield good results. Hints to a theoretical examination of the method including su cient conditions for feasibility and convergence are given.KEY WORDS: boundary element method; dual reciprocity method; radial basis functions; non-linear di erential equations
Die Randelementmethode ist zur Lösung homogener linearer Differentialgleichungen hervorragend geeignet. Hier wird ein für inhomogene Probleme ergänzendes Verfahren vorgestellt, bei dem die rechte Seite durch Radialbasisfunktionen approximiert wird und damit eine Näherung an eine spezielle Lösung aufgestellt werden kann. Im Gegensatz zu bekannten Verfahren wird dabei Quasiinterpolation statt Interpolation mit Radialbasisfunktionen verwendet. Es werden dadurch eine hohe Konvergenzordnung erreicht und bei der Interpolation entstehende Probleme vermieden. Das Verfahren ist auch zur Behandlung nichtlinearer Probleme geeignet.
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