Numerical analytic continuation on bounded domains

The problem of numerical analytic continuation of an analytic function with complex variable, in general, is ill-posed and frequently encountered in many practical applications. However, there are few results for this problem until now. In the present paper, this problem with a single complex variable is considered on bounded domains. A very simple meshless algorithm based on the method of fundamental solution (MFS) combining with numerical differentiation is established. Some numerical examples verify the feasibility and effectiveness of this method.