Kansa method for problems with multiple boundary conditions.

In the paper a kind of meshless discretization technique, called the Kansa method, is investigated in the context of problems with multiple boundary conditions. This numerical method uses interpolant composed of radial basis functions as well as collocation technique to discretize differential equations. To overcome the problem that appears for equations with multiple boundary conditions, where more equations should be associated with a boundary node than degrees of freedom that exist at this node, an extension of the method is proposed. The key idea lies in the modification of the interpolant with the use of Hermite formulation. The details of the approach are shown in the paper. Moreover, the special attention is paid to estimate respective value of the shape parameter included in radial functions to ensure stability of the solution process and high accuracy. To illustrate usefulness, accuracy and convergence of the method, it is employed to solve a test problem of the bending Kirchhoff plate. [ABSTRACT FROM AUTHOR]