A New Collocation Scheme Using Non-polynomial Basis Functions
暂无分享,去创建一个
[1] Leslie Greengard,et al. Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation , 2000, SIAM J. Numer. Anal..
[2] Jan S. Hesthaven,et al. Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators , 1998 .
[3] C. W. Clenshaw. The numerical solution of linear differential equations in Chebyshev series , 1957, Mathematical Proceedings of the Cambridge Philosophical Society.
[4] Jie Shen,et al. Spectral Approximation of the Helmholtz Equation with High Wave Numbers , 2005, SIAM J. Numer. Anal..
[5] P. Revesz. Interpolation and Approximation , 2010 .
[6] Elsayed M. E. Elbarbary,et al. Integration Preconditioning Matrix for Ultraspherical Pseudospectral Operators , 2006, SIAM J. Sci. Comput..
[7] Thomas Hagstrom,et al. An efficient spectral method for ordinary differential equations with rational function coefficients , 1996, Math. Comput..
[8] Rene F. Swarttouw,et al. Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.
[9] ShenJie. Efficient spectral-Galerkin method I , 1994 .
[10] S. E. El-gendi,et al. Chebyshev Solution of Differential, Integral and Integro-Differential Equations , 1969, Comput. J..
[11] Zhimin Zhang,et al. Superconvergence Points of Polynomial Spectral Interpolation , 2012, SIAM J. Numer. Anal..
[12] Zhimin Zhang,et al. On hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme , 2013, J. Comput. Phys..
[13] Jie Shen,et al. Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials , 1994, SIAM J. Sci. Comput..
[14] Yau Shu Wong,et al. Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates , 2015 .
[15] Francesco Aldo Costabile,et al. A Birkhoff interpolation problem and application , 2010 .
[16] L. Trefethen,et al. THE EIGENVALUES OF SECOND-ORDER SPECTRAL DIFFERENTIATION MATRICES* , 1988 .
[17] B. Mihaila,et al. Numerical approximations using Chebyshev polynomial expansions: El-gendi's method revisited , 1999, physics/9901005.
[18] Seymour V. Parter,et al. Preconditioning Chebyshev Spectral Collocation Method for Elliptic Partial Differential Equations , 1996 .
[19] Michel Deville,et al. Chebyshev pseudospectral solution of second-order elliptic equations with finite element preconditioning , 1985 .
[20] Li-Lian Wang,et al. A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix , 2013, SIAM J. Sci. Comput..
[21] Hassan Mohamed El-Hawary,et al. A chebyshev method for the solution of boundary value problems , 1991, Int. J. Comput. Math..
[22] Claudio Canuto,et al. Finite-Element Preconditioning of G-NI Spectral Methods , 2009, SIAM J. Sci. Comput..
[23] Philip W. Livermore,et al. Galerkin orthogonal polynomials , 2010, J. Comput. Phys..
[24] Leslie Greengard,et al. Spectral integration and two-point boundary value problems , 1991 .
[25] B. K. Muite,et al. A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems , 2010, J. Comput. Appl. Math..
[26] Jie Shen,et al. Fourierization of the Legendre--Galerkin method and a new space--time spectral method , 2007 .
[27] Jie Shen,et al. Optimal Spectral-Galerkin Methods Using Generalized Jacobi Polynomials , 2006, J. Sci. Comput..
[28] Jie Shen,et al. Spectral Methods: Algorithms, Analysis and Applications , 2011 .
[29] Jie Shen,et al. Generalized Jacobi polynomials/functions and their applications , 2009 .
[30] F. Ghoreishi,et al. The Tau method and a new preconditioner , 2004 .
[31] Seymour V. Parter,et al. Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators , 1997 .
[32] Suchuan Dong,et al. An eigen-based high-order expansion basis for structured spectral elements , 2011, J. Comput. Phys..
[33] Zhimin Zhang,et al. Superconvergence of Jacobi–Gauss-Type Spectral Interpolation , 2014, J. Sci. Comput..
[34] Michel O. Deville,et al. Finite-Element Preconditioning for Pseudospectral Solutions of Elliptic Problems , 1990, SIAM J. Sci. Comput..
[35] T. Hagstrom,et al. Integration preconditioners for differential operators in spectral r-methods , 2011 .
[36] Claudio Canuto,et al. Preconditioned minimal residual methods for Chebyshev spectral calculations , 1985 .
[37] Kate Smith-Miles,et al. Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices , 2013, J. Comput. Appl. Math..
[38] Weiwei Sun,et al. Convergence Analysis of Spectral Collocation Methods for a Singular Differential Equation , 2003, SIAM J. Numer. Anal..