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Abstract
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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.
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