A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

作者：Shivanian Elyas

来源：Zeitschrift fur Naturforschung Section A-A Journal of Physical Sciences, 2015, 70(8): 673-682.

DOI：10.1515/zna-2015-0100

<jats:title>Abstract</jats:title><jats:p>This paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.</jats:p>

• 出版日期2015-8