Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation
Journal of Approximation Theory
Applied Mathematics and Computation
Mathematical treatment of the magnetic confinement in a current carrying stellarator
Nonlinear Analysis: Theory, Methods & Applications
Journal of Computational Physics
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
Finite-difference methods for solution of nonlocal boundary value problems
Computers & Mathematics with Applications
Radial basis collocation methods for elliptic boundary value problems
Computers & Mathematics with Applications
The role of the multiquadric shape parameters in solving elliptic partial differential equations
Computers & Mathematics with Applications
An alternative procedure for selecting a good value for the parameter c in RBF-interpolation
Advances in Computational Mathematics
Applied Numerical Mathematics
Applied Numerical Mathematics
On the solution of a nonlocal problem
Computers & Mathematics with Applications
A meshless method for the numerical computation of the solution of steady Burgers-type equations
Applied Numerical Mathematics
Error estimates and condition numbers for radial basis function interpolation
Advances in Computational Mathematics
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The development of numerical methods for the solution of partial differential equations (PDEs) with nonlocal boundary conditions is important, since such type of problems arise as mathematical models of various real-world processes. We use radial basis function (RBF) collocation technique for the solution of a multidimensional linear elliptic equation with classical Dirichlet boundary condition and nonlocal integral conditions. RBF-based meshless methods are easily implemented and efficient, especially for multidimensional problems formulated on complexly shaped domains. In this paper, properties of the method are investigated by studying two- and three-dimensional test examples with manufactured solutions. We analyze the influence of the RBF shape parameter and the distribution of the nodes on the accuracy of the method as well as the influence of nonlocal conditions on the conditioning of the collocation matrix.