Application of a kernel method with stably evaluated Gaussian kernel to problems on irregular domains.

The paper extends recently developed idea of stable evaluation of the Gaussian kernel. Owing to this, the Gaussian radial basis function that is sensitive to the shape parameter can be stably evaluated and applied to interpolation problems as well as to solve differential equations, giving highly accurate results. But it can be done only with grids being the Cartesian product of sets of points, what limits the use of this idea to rectangular domains. In the present paper, by the association of an appropriate transformation with the mentioned method, the latter is applied to solve differential equations on quadrilateral irregular domains. As an example a biharmonic problem is taken into consideration. The numerical tests show high accuracy and usefulness of the method.. [ABSTRACT FROM AUTHOR]