Multiquadrics – a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations. (English) Zbl 0850.76048


76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76M99 Basic methods in fluid mechanics
65Z05 Applications to the sciences


Zbl 0692.76003
Full Text: DOI


[1] Kansa, E. J., Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—I. Surface approximations and partial derivative estimates, Computers Math. Applic., 19, 8/9, 127-145 (1990) · Zbl 0692.76003
[2] Franke, R., Scattered data interpolation: test of some other methods, Math. Comput., 38, 181-200 (1982) · Zbl 0476.65005
[4] Hardy, R. L., Research results in the application of multiquadratic equations to surveying and mapping problems, Surv. Mapp., 35, 321-332 (1975)
[5] Stead, S., Estimation of gradients from scattered data, Rocky Mount. J. Math., 14, 265-279 (1984) · Zbl 0558.65009
[6] Micchelli, C. A., Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constr. Approx., 2, 11-22 (1986) · Zbl 0625.41005
[8] Adams, E., (VII Int. Conf. Computational Methods in Water Resources (June 1988), MIT Press: MIT Press Cambridge, Mass)
[9] Kansa, E. J., Highly accurate shock flow calculations with moving grids and mesh refinement, (Vichnevetsky, R.; Vignes, J., Numerical Mathematics and Applications (1986), North Holland: North Holland New York), 311-316 · Zbl 1185.65178
[10] von Neumann, J., (Traub, A. K., John von Neumann, Collected Works, Vol. 6 (1963), MacMillan: MacMillan New York), 219-237
[11] Kansa, E. J., Application of Hardy’s multiquadratic interpolation to hydrodynamics, (Proc. 1986 Simul Conf., Vol. 4 (1986)), 111-117
[12] Braess, D., The contraction number of a multigrid method for solving the Poisson equation, Numer. Math., 37, 387-404 (1981) · Zbl 0461.65078
[13] Braess, D., The convergence rate of a multigrid method relaxation for the Poisson equation with Gauss-Seidel relaxation for the Poisson equation, Math. Comput., 42, 505-519 (1984) · Zbl 0539.65075
[14] Braess, D.; Hackbusch, W., A new convergence proof for the multigrid method including the V-cycle, SIAM Jl numer. Analysis, 20, 967-975 (1983) · Zbl 0521.65079
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.