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A matrix decomposition RBF algorithm: Approximation of functions and their derivatives
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 theExpand
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Numerical analysis of the MFS for certain harmonic problems
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 matricesExpand
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Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation
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 aExpand
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Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
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 ofExpand
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Linearly implicit schemes for a class of dispersive–dissipative systems
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.Expand
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Matrix decomposition RBF algorithm for solving 3D elliptic problems
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 basisExpand
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A matrix decomposition MFS algorithm for axisymmetric potential problems
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 thisExpand
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The Method of Fundamental Solutions: A Weighted Least-Squares Approach
We investigate the Method of Fundamental Solutions (MFS) for the solution of certain elliptic boundary value problems. In particular, we study the case in which the number of collocation pointsExpand
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Some Aspects of the Method of Fundamental Solutions for Certain Biharmonic Problems
In this study, we investigate the application of the Method of Fundamental Solutions for the solution of biharmonic Dirichlet problems on a disk. Modifications of the method for overcoming sources ofExpand
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The under-determined version of the MFS: Taking more sources than collocation points
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 theExpand
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