Boundary Knot Method for Convection-diffusion Problems

The boundary knot method (BKM) is meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial diferential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial articial boundary outside the physical domain. The purpose of this paper is use of BKM to solve convection–diffusion problem. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability.