In this paper‎, ‎we decide to select the best center nodes‎ ‎of radial basis functions by applying the Multiple Criteria Decision‎ ‎Making (MCDM) techniques‎. ‎Two methods based on radial basis‎ ‎functions to approximate the solution of partial differential‎ ‎equation by using collocation method are applied‎. ‎The first is based‎ ‎on the Kansa's approach‎, ‎and the second is based on the Hermit...

In this paper, we mainly study the superconvergence properties in approximation of second- and third-order BVPs by spectral collocation methods. The theoretical analyses identify points interpolation function. Ample numerical experiments are carried out which perfectly match results. addition, results show that also hold solving PDEs.

Multiple orthogonal polynomials are polynomials in one variable that satisfy orthogonality conditions with respect to several measures. I will briefly give some general properties of these polynomials (recurrence relation, zeros, etc.). These polynomials have recently appeared in many applications, such as number theory, random matrices, non-intersecting random paths, integrable systems, etc. I...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

In this paper we examine the computation of the potential generated by space-time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the cur...