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A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
Author(s) -
Sarra Scott A.
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20290
Subject(s) - collocation (remote sensing) , mathematics , eigenvalues and eigenvectors , radial basis function , collocation method , orthogonal collocation , stability (learning theory) , boundary (topology) , partial differential equation , function (biology) , mathematical analysis , boundary value problem , differential equation , computer science , ordinary differential equation , physics , quantum mechanics , machine learning , evolutionary biology , artificial neural network , biology
Differentiation matrices associated with radial basis function (RBF) collocation methods often have eigenvalues with positive real parts of significant magnitude. This prevents the use of the methods for time‐dependent problems, particulary if explicit time integration schemes are employed. In this work, accuracy and eigenvalue stability of symmetric and asymmetric RBF collocation methods are numerically explored for some model hyperbolic initial boundary value problems in one and two dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008