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Radial basis function methods are powerful tools in numerical analysis andhave demonstrated good properties in many different simulations. However, fortime-dependent partial differential equations, only a few stability results areknown. In particular, if boundary conditions are included, stability issuesfrequently occur. The question we address in this paper is how provablestability for RBF methods can be obtained. We develop and constructenergy-stable radial basis function methods using the general framework ofsummation-by-parts operators often used in the Finite Difference and FiniteElement communities.

Energy-stable global radial basis function methods on summation-by-parts form