Convergence of general meshless Schwarz method using radial basis functions

In this paper, we provide the theoretical justification of general meshless Schwarz method using radial basis functions. Using this meshless method, we only need to solve many small problems instead of one big ill-conditioned problem, and get the results with almost the same accurate. The only premise we need in our meshless method is that the resultant coefficient matrix of the linear algebra equations which we got when we solve the partial differential equations is positive definite, and which can usually be satisfied if we use meshless Galerkin method or meshless Hermitian–Birkhoff's collocation method.