Solving nonlinear differential equations of mechanics with the boundary element method and radial basis functions

Abstract

The Boundary Element Method is a very effective method for solving linear differential equations. To use it also in the consideration of non-linear problems some different 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 differential equations of the kind Δmu = 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 sufficient conditions for feasibility and convergence are given.