Exact explicit time integration of hyperbolic partial differential equations with mesh free radial basis functions

Engineering Analysis with Boundary Elements

Volumn 31, Issue 7, 2007, Pages 577-585

  Kansa, E J ^a  

^a University of California   (United States)

Author keywords

Exact explicit time solutions; Hyperbolic PDEs; Linearized ODE systems; Moving data centers; Radial basis functions

Indexed keywords

INTEGRATION; MATHEMATICAL TRANSFORMATIONS; MEAN SQUARE ERROR; ORDINARY DIFFERENTIAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS;

EXACT EXPLICIT TIME SOLUTIONS; EXPANSION COEFFICIENTS; HYPERBOLIC EQUATIONS; MOVING DATA CENTERS; NUMERICAL SOLUTIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34249709499     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2006.12.001     Document Type: Article

References (20)

1. Fedoseyev A.I., Friedman M.J., and Kansa E.J. Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary. Comput Math Appl 43 3-5 (2002) 491-500
2. Cheng A.H.D., Golberg M.A., Kansa E.J., and Zammito T. Exponential convergence and h-c multiquadric collocation method for partial differential equations. Numer Meth PDEs 19 (2003) 571-594
3. Wu Y.L., and Shu C. Development of RBF-DQ method for derivative approximation and its application to simulate natural convection in concentric annuli. Comput Mech 29 (2002) 477-485
4. Shu C., Ding H., and Yeo K.S. Local radial basis function based differential quadrature method and its applications to solve two-dimensional incompressible Navier-Stokes equations. Comput Meth Appl Mech Eng 192 (2003) 941-954
5. Franke R. Scattered data interpolation: tests of some methods. Math Comput 38 (1982) 181-200
6. Madych W.R., and Nelson S.A. Multivariate interpolation and conditionally positive definite functions. Approx Theory Appl 4 (1988) 77-89
7. Madych W.R. Miscellaneous error bounds for multiquadric and related interpolators. Comput Math Appl 24 12 (1992) 121-138
8. Kansa E.J. Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics: II. Solutions to parabolic hyperbolic and elliptic partial differential equations. Comput Math Appl 19 6-8 (1990) 147-161
9. Ling L., and Kansa E.J. A least squares preconditioner for radial basis functions collocation methods. Adv Comput Math 12 (2005) 31-54
10. Ling L., and Kansa E.J. Preconditioning for radial basis functions with domain decomposition. Math Comput Model 40 (2004) 1413-1427
11. Brown D., Ling L., Kansa E.J., and Levesley J. On approximate cardinal preconditioning methods for radial functions. Eng Anal Boundary Elem 29 (2005) 343-353
12. Kansa E.J. Local, point-wise rotational transformation of the conservation equations into stream-wise coordinates. Comput Math Appl 43 3-5 (2002) 501-512
13. Kansa E.J., Power H., Fasshauer G.E., and Ling L. A volumetric integral radial basis function method for time-dependent partial differential equations: I. Formulation. Eng Anal Boundary Elem 28 (2004) 1191-1206
14. Ling L., and Hon Y.C. Improved numerical solver for Kansa's method based on affine space decomposition. Eng Anal Boundary Elem 29 (2005) 1077-1085
15. Moridis G.J., and Kansa E.J. The Laplace transform multiquadric method: a highly accurate scheme for the numerical solution of linear partial differential equations. J Appl Sci Comput 1 2 (1994) 375-407
16. Wang J.G., and Liu G.R. On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput Meth Appl Mech Eng 191 (2002) 2611-2630
17. Xiao J.R., Gama B.A., Gillespie Jr. J.W., and Kansa E.J. Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions. Eng Anal Boundary Elem 29 (2005) 95-106
18. Wertz J., Kansa E.J., and Ling L. The role of the multiquadric shape parameters in solving elliptic partial differential equations. Comput Math Appl 51 8 (2006) 1335-1348
19. Kansa E.J., and Hon Y.C. Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput Math Appl 39 7/8 (2000) 123-137
20. Ingber M.S., Chen C.S., and Tanski J.A. A mesh free approach using radial basis functions and parallel domain decomposition for solving three dimensional diffusion equations. Int J Numer Meth Eng 60 (2004) 2183-2201