A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs

Numerical Methods for Partial Differential Equations

Volumn 24, Issue 2, 2008, Pages 670-686

  Sarra, Scott A ^a  

^a MARSHALL UNIVERSITY   (United States)

Author keywords

Collocation methods; Eigenvalue stability; Hyperbolic partial differential equations; Numerical partial differential equations; Radial basis functions

Indexed keywords

EID: 40749138583     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20290     Document Type: Article

References (14)

1. 1 E. Kansa, Multiquadrics—a scattered data approximation scheme with applications to computational fluid dynamics (II): Solutions to parabolic, hyperbolic, and elliptic partial differential equations, Computers Math Applic 19 ( 1990), 147–161.
2. 2 G. E. Fasshauer, Solving partial differential equations by collocation with radial basis functions, Proceedings of Chamonix, 1996.
3. 3 G. E. Fasshauer, RBF collocation methods and pseudospectral methods, Preprint. Illinois Institute of Technology, 2004.
4. 4 B. Fornberg, T. Dirscol, G. Wright, and R. Charles, Observations on the behavior of radial basis function approximations near boundaries, Computers Math Applic 43 ( 2003), 473–490.
5. 5 R. Platte and T. Driscoll, Eigenvalue stability of radial basis functions discretizations for time‐dependent problems, Computers Math Applic 51 ( 2006), 1251–1268.
6. 6 F. Q. Hu, M. Y. Hussaini, and J. L. Manthey, Low‐dissipation and low‐dispersion Runge‐Kutta schemes for computational acoustics, J Computat Phys 124 ( 1996), 177–191.
7. 7 R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Adv Computat Math 3 ( 1995), 251–264.
8. 8 M. D. Buhmann, Radial Basis Functions, Cambridge University Press, 2003.
9. 9 C. Micchelli, Interpolation of scattered data: distance matrices and conditionally positive definite functions, Construct Approxim 2 ( 1986), 11–22.
10. 10 Y. Hon and R. Schaback, On unsymmetric collocation by radial basis function, Appl Math Computations 119 ( 2001), 177–186.
11. 11 N. Flyer and G. Wright, Transport schemes on a sphere using radial basis functions, J Computat Phys, submitted for publication.
12. 12 S. De Marchi, R. Schaback, and H. Wendland, Near‐optimal data‐independent point locations for radial basis function interpolation, Adv Computat Math 23 ( 2005), 317–330.
13. 13 A. Taflove and S. Hagness, Computational electrodynamics: The finite‐difference time‐domain method, 2nd Ed., Artech House Publishers, 2000.
14. 14 S. A. Sarra and A. Aluthge, Computational mode control, expanded stability, and second order accuracy with leap‐frog time differencing via symmetric filtering, J Computat Appl Math, under review.