An approximation method for solving inhomogeneous linear and nonlinear differential equations using the boundary element method and radial basis functions

The boundary element method Is very useful to solve homogeneous linear differential equations. Here as an extension to inhomogeneous problems a method is presented in which the right hand side is approximated by radial basis functions leading to an approximation of a special solution. Contrary to known methods use technique of quasiinterpolation, is used instead of interpolation with radial basis functions. This yields a high order of convergence and avoids problems connected with the interpolation. The approach allows also the solution, of nonlinear differential equations.