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We propose an efficient algorithm for the approximation of functions and their derivatives using radial basis functions (RBFs). The interpolation points are placed on concentric circles and the… (More)
The method of fundamental solutions is a boundary-type meshless method for the solution of certain elliptic boundary value problems. By exploiting the structure of the matrices appearing when this… (More)
We consider the periodic initial value problem for the Kuramoto-Sivashinsky (KS) equation. We approximate the solution by discretizing in time by implicit-explicit BDF schemes and in space by a… (More)
The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices… (More)
We consider initial value problems for semilinear parabolic equations, which possess a dispersive term, nonlocal in general. This dispersive term is not necessarily dominated by the dissipative term.… (More)
In this study, we propose an efficient algorithm for the evaluation of the particular solutions of three-dimensional inhomogeneous elliptic partial differential equations using radial basis… (More)
In this study we investigate the approximation of the solutions of certain elliptic boundary value problems by the Method of Fundamental Solutions (MFS). In particular, we study the case in which the… (More)
The flow of two superposed fluids in a channel in the presence of an insoluble surfactant is studied. Asymptotic analysis when one of the layers is thin yields a system of coupled weakly non-linear… (More)
In this work, we propose an efficient matrix decomposition algorithm for the Method of Fundamental Solutions when applied to three-dimensional boundary value problems governed by elliptic systems of… (More)