Multiquadric finite difference (MQ-FD) method and its application

Advances in Applied Mathematics and Mechanics

Volumn 1, Issue 5, 2009, Pages 615-638

  Shan, Yong Yuan ^a   Shu, Chang ^a   Qin, Ning ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Central FD method.; MQ FD method; Shape parameter

Indexed keywords

EID: 78650796062     PISSN: 20700733     EISSN: 20751354     Source Type: Journal    
DOI: 10.4208/aamm.09-m0942     Document Type: Article

References (16)

1. E. J. Kansa, Multiquadrics A scattered data approximation scheme with application to computational fluid dynamics-I. Surface approximations and partial derivative estimates, Comput. Math. Appl., 19 (1990), pp. 127-145.
2. E. J. Kansa, Multiquadrics, A scattered data approximation scheme with application to computational fluid dynamics-II. Solutions to parabolic, hyperbolic, and elliptic partial differential equations, Comput. Math. Appl., 19 (1990), pp. 147-161.
3. G. E. Fasshauer, Solving partial differential equations by collocation with radial basis functions, in: A.L. Mehaute, C. Rabut, L. L. Schumaker (Eds.), Surface Fitting and Multiresolution Methods, 1997, pp. 131-138.
4. C. Franke and R. Schaback, Solving partial differential equations with radial basis functions: multilevel methods and smoothing, Adv. Comput. Math., 11 (1999), pp. 139-159.
5. X. Zhang, K. Z. Song, M. W. Lu and X. Liu, Meshless methods based on collocation with radial basis functions, Comput. Mech., 26 (2000), pp. 333-343.
6. W. Chen, New RBF collocation schemes and kernel RBFs with applications, Lecture Notes in Computational Science and Engineering, 26 (2002), pp. 75-86.
7. W. Chen and M. Tanaka, A meshless, integration-free, and boundary-only RBF technique, Comput. Math. Appl., 43 (2002), pp. 379-391.
8. C. S. Chen and C. A. Brebbia, Dual reciprocity method using for Helmholtz-type operators, Boundary Elements, 20 (1998), pp. 495-504.
9. C. Shu, H. Ding and K. S. Yeo, Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 941-954.
10. R. E. Bellman and J. Casti, Differential quadrature and long term integration, J. Math. Anal. Appl., 34 (1971), pp. 235-238.
11. R. E. Bellman, B. G. Kashef and J. Casti, Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations, J. Comput. Phys., 10 (1972), pp. 40-52.
12. R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res., 76 (1971), pp. 1905-1915.
13. R. Franke, Scattered data interpolation: tests of some methods, Math. Comp., 38 (1982), pp. 181-199.
14. R.L. Hardy, Theory and applications of the multiquadric-biharmonic method: 20 years of discovery, Comput. Math. Appl., 19 (1990), pp. 163-208.
15. 2 in multiquadric interpolation, Computer Math. Applic., 21 (1991), pp. 29-42.
16. U. Ghia, K. N. Ghia and C.T. Shin, High-Resolutions for incompressible flow using the Navier-Stokes equations and a multi-grid method, J. Comput. Phys., 48 (1982), pp. 387-411.