On invariance of schemes in the method of fundamental solutions

Method of fundamental solutions (MFS) is a meshfree numerical solver for linear homogeneous partial differential equations, and it has been applied to several problems. It is well known that some numerical solutions by MFS do not satisfy invariance properties, which is unnatural from viewpoint of physics. In this paper, we propose a unified way to obtain invariant schemes for MFS. The key idea is to introduce scaling factors.