Abstract. A few novel radial basis function (RBF) discretization schemes for partial differential equations are developed in this study. For boundary-type methods, we derive the indirect and direct symmetric boundary knot methods. Based on the multiple reciprocity principle, the boundary particle method is introduced for general inhomogeneous problems without using inner nodes. For domain-type ...

Biharmonic equation is one of the most existing operator in many areas, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper we deal with the use of the local particular solution method to solve the two-dimensional biharmonic equation in a bounded region. The technique is based on decoupling the biharmoni...

There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at benefits overtesting by using more collocation conditions than number basis functions. Overtesting not only reduces problem size, but is also known to be necessary stability convergence widely used unsymmetric Kansa-type strong-form methods. We consider kernel-...

We employ a Kansa-radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains. This discretization leads, with an appropriate selection of collocation points and for any choice of RBF, to linear systems in which the matrices possess block circulant structures. These linear systems can be solved efficiently using matrix decomposition algor...

Although most work to date on RBFs relates to scattered data approximation and in general to interpolation theory, there has recently been an increased interest in their use for solving partial differential equations (PDEs). This approach, which approximates the whole solution of the PDE directly using RBFs, is very attractive due to the fact that this is truly a mesh-free technique. Kansa [1] ...

We present a case study of data integration and reuse involving one dozen researchers who published datasets in Open Context, an online data publishing platform, as part of collaborative archaeological research on early domesticated animals in Anatolia. Our discussion reports on how different editorial and collaborative review processes improved data documentation and quality, and created ontol...