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The Hermite collocation method using radial basis functions. (English) Zbl 0967.65107
Summary: In this note, numerical experiments are carried out to study the convergence of the Hermite collocation method using high-order polyharmonic splines and H. Wendland’s radial basis functions [Adv. Comput. Math. 4, No. 4, 389-396 (1995; Zbl 0838.41014); J. Approx. Theory 93, No. 2, 258-272 (1997; Zbl 0904.41013)].

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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[1] Duchon, J., Sur l’erreur d’interpolation des functions de plusiers variables par LES dm-splines, RAIRO anal numer, 12, 4, 325-334, (1978) · Zbl 0403.41003
[2] Fasshauer, G.E., Solving partial differential equations by collocation with radial basis functions, () · Zbl 0938.65140
[3] Fasshauer, G.E., Solving differential equations with radial basis functions: multilevel methods and smoothing, Adv comput math, 11, 2/3, 139-159, (1999) · Zbl 0940.65122
[4] Franke, C.; Schaback, R., Convergence orders of meshless collocation methods using radial basis functions, Adv comput math, 93, 73-82, (1998) · Zbl 0943.65133
[5] Hon YC, Schaback R. On nonsymmetric colloration by radial basis functions. Appl Math Comput (accepted).
[6] Kansa, 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, 149-161, (1990) · Zbl 0850.76048
[7] Light, W.; Wayne, H., Error estimates for approximation by radial basis functions, (), 215-246 · Zbl 0843.41005
[8] Luo, Z.; Levesley, J., Error estimates and convergence rates for variational Hermite interpolation, J approx theor, 95, 264-279, (1998) · Zbl 0915.41002
[9] Muleskov, A.S.; Golberg, M.A.; Chen, C.S., Particular solutions of Helmholtz-type operators using higher order polyharmonic splines, Comput mech, 23, 411-419, (1999) · Zbl 0938.65139
[10] Wendland, H., Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Adv comput math, 4, 389-396, (1995) · Zbl 0838.41014
[11] Wendland, H., Error estimates for interpolation by compactly supported radial basis functions of minimal degree, J approx theor, 93, 2, 258-272, (1997) · Zbl 0904.41013
[12] Wu, Z., Hermite-Birkhoff interpolation of scattered data by radial basis functions, Approx theor appl, 8, 2, 1-10, (1992) · Zbl 0757.41009
[13] Wu, Z.; Schaback, R., Local error estimates for radial basis function interpolation of scattered data, IMA J numer anal, 13, 13-27, (1993) · Zbl 0762.41006
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