Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains

The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in bounded domain. It demonstrated by combining shifted points outside domain and determining coefficients linear sum satisfy boundary condition on finite boundary. In this paper, existence MFS Neumann problems modified Helmholtz disk domains rigorously demonstrated. We reveal sufficient solution. Applying Green formula problem equation, we bound error between exact into difference function normal derivative integrations. Using estimate error, show convergence with exponential order, that is, N2aN where positive constant less than one N number collocation points. Furthermore, it tends 0 order numerical simulations increasing N.