Multiquadric collocation method with integralformulation for boundary layer problems

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  R. L. Hardy Multiquadric equations of topography and other irregular surfaces , 1971 .

[3]  Eugene C. Gartland,et al.  Graded-mesh difference schemes for singularly perturbed two-point boundary value problems , 1988 .

[4]  W. Madych,et al.  Multivariate interpolation and condi-tionally positive definite functions , 1988 .

[5]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[6]  E. Kansa MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[7]  E. Kansa Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[8]  M. Buhmann Multivariate cardinal interpolation with radial-basis functions , 1990 .

[9]  R. L. Hardy Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 , 1990 .

[10]  M. Buhmann Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics , 1990 .

[11]  W. R. Madych,et al.  Miscellaneous error bounds for multiquadric and related interpolators , 1992 .

[12]  G. J. Moridis,et al.  The Laplace Transform Multiquadric Method: A Highly Accurate Scheme for the Numerical Solution of Partial Differential Equations , 1993 .

[13]  Eugene O'Riordan,et al.  On piecewise-uniform meshes for upwind- and central-difference operators for solving singularly perturbed problems , 1995 .

[14]  Tao Tang,et al.  Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems , 1996, SIAM J. Sci. Comput..

[15]  X. Z. Mao,et al.  A Multiquadric Interpolation Method for Solving Initial Value Problems , 1997 .

[16]  Benny Y. C. Hon,et al.  An efficient numerical scheme for Burgers' equation , 1998, Appl. Math. Comput..

[17]  Richard K. Beatson,et al.  Fast fitting of radial basis functions: Methods based on preconditioned GMRES iteration , 1999, Adv. Comput. Math..

[18]  E. J. Kansa,et al.  Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme , 1999 .

[19]  E. Kansa,et al.  Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations , 2000 .

[20]  Nam Mai-Duy,et al.  Numerical solution of differential equations using multiquadric radial basis function networks , 2001, Neural Networks.

[21]  Cameron Thomas Mouat Fast algorithms and preconditioning techniques for fitting radial basis functions. , 2001 .

[22]  Jungho Yoon,et al.  Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space , 2001, SIAM J. Math. Anal..

[23]  Richard K. Beatson,et al.  Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods , 2000, SIAM J. Sci. Comput..

[24]  Nam Mai-Duy,et al.  Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks , 2001 .

[25]  E. Kansa,et al.  Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary , 2002 .

[26]  Y. Hon,et al.  Overlapping domain decomposition method by radial basis functions , 2003 .

[27]  Leevan Ling Radial basis functions in scientific computing , 2003 .

[28]  Leevan Ling,et al.  A volumetric integral radial basis function method for time-dependent partial differential equations. I. Formulation , 2004 .

[29]  Leevan Ling,et al.  A least-squares preconditioner for radial basis functions collocation methods , 2005, Adv. Comput. Math..