This talk will be on numerical solution methods for PDE:s in 2D,based upon integral equations,which in certain cases outperform other solution strategies such as the finite element method by a wide margin.Integral equation methods are extremely accurate and for homogenous problems such as for example Laplaces equation only the boundary needs to be discretized,greatly reducing the number of unknowns needed to solve for.No claim is made for these methods to match the versatility of FEM,rather the moral is that depending on the problem at hand it can be very beneficial,and sometimes vital,to be aware of and choose the correct solution strategy.