Ahmad Shirzadi

This paper is concerned with the development of ameshless local approach based on the finite collocation method for solving Cauchy problems of 2-D elliptic PDEs in annulus domains. In the proposed approach, besides the collocation of unknown solution, the governing equation is also enforced in the local domains. Moreover, to improve the accuracy, the method considers auxiliary points in local subdomains and imposes the governing PDE operator at these points, without changing the global system size. Localization property of the method reduces the ill-conditioning of the problem and makes it efficient for Cauchy problem. To show the efficiency of the method, four test problems containing Laplace, Poisson, Helmholtz and modified Helmholtz equations are given. A numerical comparison with traditional local RBF method is given in the first test problem.