A Study on Radial Basis Function and Quasi-Monte Carlo Methods

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 1, Issue 4, 2000, Pages 337-342

  Chen, W ^a   He, J H ^b  

^a SHINSHU UNIVERSITY   (Japan)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Edge effects; Error bound; GS RBF; Kernel function; Quasi Monte Carlo method; Radial basis function; Time space RBF

Indexed keywords

EID: 0034550314     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2000.1.4.337     Document Type: Article

References (11)

1. Franke, C. and Schaback, R., Solving partial differential equation by collocation using radial basis function, Appl. Math. Comput. 93(1998), 73-82.
2. Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods, SIAM, CBMS 63, Philadelphia, PA, 1992.
3. Chen, C.S., Golberg, M.A. and Hon, Y.C., The method of fundamental solutions and quasi-monte-carlo method for diffusion equations, Int. J. Numer. Meth. Engng., 43(1998), 1421-1435.
4. Chen, W. and Tanaka, M, New insights in boundary-only and domain-type RBF methods, Inter. J. Nonlinear Sci Numer. Simulation, 3(2000), 145-152.
5. 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. Appls., 39(2000) 123-137.
6. Duchon, J., Splines minimizing rotation invariant semi-norms in Sobolov spaces, in: "Constructive Theory of Functions of Several Variables", Springer-Verlag, Berlin, 1976.
7. Powell, M.J.D., Recent advances in Cambridge on radial basis functions, The Second Inter. Dortmunt Meeting on Approximation Theory, 1998.
8. Fedoseyev, A.I., Friedman, M.J. and Kansa, E.J., Continuation for nonlinear elliptic partial differential equations discretized by the multiquadric method, to appear in Int. J. Bifur. Chaos 10(2000).
9. Fedoseyev, A.I., Friedman, M.J. and Kansa, E.J., Improved multiquadratic method for elliptic partial differential equations via PDE collocation on the boundary, Comput. Math. Appl., (submitted), 2000.
10. G. Ramm, Theory and Applications of Some New Classes of Integral Equations, Springer-Verlag, New York, 1980.
11. Thompson, J.F., Thames, F.C., and Mastin, C.W., Automatic numerical generation of body-fitted curvilinear coordinate system for field containing vary number of arbitrary tow-dimensional bodies, J. Comput. Phys., 15(1974), 299-319.