Y.C. Hon and X.Z. Mao, An efficient numerical scheme for Burgers' equation, to appear at the Journal of Applied Mathematics and Computation. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Continuation for Nonlinear Elliptic Partial.. - Fedoseyev, Friedman.. (1 citation) (Correct)
....121, set of nodes, while locally adapting the shape parameter c j . The multi zone method of Wong et al. 46] is yet another alternative method for improving computational efficiency. This method is readily parallelizable, and the conditioning of the resulting matrices are much better. Hon and Mao [26] showed that an adaptive algorithm that adjusted the nodes to follow the peak of the shock wave can produce accurate results in 1D Burgers equation with only 10 nodes, even for steep shocks with Re = 10 4 . 3 Discretization of nonlinear elliptic PDEs by the MQ method. We consider the second ....
Y.C. Hon, and X.Z. Mao, An efficient numerical scheme for Burgers equation, Appl.Math. Comp., 95 (1998), 37-50.
Solving Differential Equations with Radial Basis Functions.. - Fasshauer (1 citation) (Correct)
.... this has been the most popular approach thus far (see [12, 13, 14, 16, 17, 22, 23, 31, 34, 36, 37, 42] Collocation also plays a key role in the dual reciprocity method (see e.g. 6, 7, 25] the moving node scheme of Djokovi c and van Damme (see [9, 10] and Hon and Mao s adaptive method [30] all briefly discussed in Section 3.3. Except for [7, 17, 22, 23, 25, 34] all of the above mentioned papers make use of globally supported RBFs, and [17] is the only paper in which a multilevel scheme is considered. 3.1.1. The Two Basic Approaches There are two different approaches taken in the ....
....can be used. In most of the cases this has been done using globally supported basis functions. The use of locally supported functions was suggested in [7] but without incorporating them in a multilevel scheme. Time dependent problems have also been considered by various authors. Hon and Mao [30] study the numerical solution of Burgers equation. They use forward differences to discretize the time derivative, and then (at each time step) non symmetric collocation based on multiquadrics to solve the spatial part. By using a strategy which moves the interpolation nodes with the shock they ....
Hon, Y. C. and X. Z. Mao, An efficient numerical scheme for Burgers' equation, Appl. Math. Comput. 95 (1998), 37--50.
Radial Basis Function Approximations as Smoothing Splines - Fred Hickernell Department (1999) Self-citation (Hon) (Correct)
....method, the multiquadric function always produces a minimal semi norm error as proven by Madych and Nelson [11] Recently, the RBFs method has been attracting more researchers on studying its application to solving ODEs and PDEs problems. Refer to Dubal et al. 12] Kansa [13, 14] and Hon et al. [15, 16, 17] for some of these examples. An interesting application of the RBFs to Artificial Intelligence can also be found in a paper given by Girosi [18] The purpose of this article is to show that for many choices of the radial basis function g, the resulting approximation can be interpreted as a ....
Y.C. Hon and X.Z. Mao, An efficient numerical scheme for Burgers' equation, to appear at the Journal of Applied Mathematics and Computation.
An Efficient Numerical Scheme for Solving Initial and Boundary.. - Ms Mao Hon Self-citation (Hon Mao) (Correct)
No context found.
Hon, Y.C. and Mao, X.Z. (1998), "An efficient numerical scheme for Burgers' equations", Appl. Math. Comp., Vol. 95, pp. 37-50.
Circumventing the ill-conditioning problem with multiquadric.. - Kansa, Hon (1998) (6 citations) Self-citation (Hon) (Correct)
No context found.
Hon, Y.C. and X.Z. Mao, 'An efficient numerical scheme for Burgers equation',, Appl. Math. Comput., 95, 37-50, (1998).
A Multiquadric Solution for the Shallow Water Equations - Yiu-Chung Hon Kwok (1999) (4 citations) Self-citation (Hon Mao) (Correct)
....suitable for solving parabolic, hyperbolic and elliptic partial differential equations. Golberg and Chen [11] combined the dual reciprocity method and the multiquadric method to approximate the particular solutions of partial differential equations. Based on this multiquadric method, Hon et al. [12,13, 14] provided an efficient numerical scheme for solving various nonlinear initial and boundary value problems including Burgers s equation with Reynolds number ranging from 0.1 to 10,000. However, the performance of the multiquadric method depends on the choice of a user specified parameter r, ....
Hon, Y.C. and Mao, X.Z. (1995), "An efficient numerical scheme for Burgers' equations ", City Univeristy of Hong Kong, Research Report MA-95-16 and has been accepted to publish at J. Appl. Math. Comp. 17
On Unsymmetric Collocation by Radial Basis Functions - Hon City University (5 citations) Self-citation (Hon) (Correct)
.... for more general settings) by several other authors, e.g. 1, 2, 3, 14] Hon et al. further extended the use of the MQ RBFs on the numerical solutions of various ordinary and partial differential equations including general initial value problems [9] nonlinear Burgers equation with shock wave [10], surface wind field computation from scattered data [5] complicated biphasic and triphasic models of mixtures [7] 8] shallow water equation for tide and currents simulation under irregular boundary [6] and free boundary problems like American option pricing [11] The computations showed the ....
Hon, Y.C. and X.Z.Mao, An efficient numerical scheme for Burgers' equation, Appl. Math. Comput. 95 (1988), 37--50.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC