Results 1 to 10 of about 57,797 (88)
Spectral collocation methods [PDF]
Applied Numerical Mathematics, 1989 This review covers the theory and application of spectral collocation methods. Section 1 describes the fundamentals, and summarizes results pertaining to spectral approximations of functions.
Hussaini, M. Y. +2 more
core +4 more sources
Efficient implementation of Radau collocation methods [PDF]
Applied Numerical Mathematics, 2013 In this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems.
Brugnano, L. +2 more
core +7 more sources
Stochastic Collocation on Unstructured Multivariate Meshes
Communications in Computational Physics, 2015 Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming ...
Akil Narayan
exaly +3 more sources
ISOGEOMETRIC COLLOCATION METHODS [PDF]
Mathematical Models and Methods in Applied Sciences, 2010 We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions.
F Auricchio +4 more
openaire +3 more sources
Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework [PDF]
Journal of Scientific Computing, 2012 In this paper, we present the first reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced Collocation Method (ERCM). This work provides a reduced basis strategy to practitioners who {prefer} a collocation,
Sigal Gottlieb, Yanlai Chen
openaire +3 more sources
Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations [PDF]
, 2011 We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such ...
Benítez, Rafael, Bolós, Vicente J.
core +2 more sources
Convergence of spectral methods for hyperbolic initial-boundary value systems [PDF]
, 1987 A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as ...
Gottlieb, D., Lustman, L., Tadmor, E.
core +2 more sources
Discontinuous collocation methods and gravitational self-force applications
, 2021 Numerical simulations of extereme mass ratio inspirals, the mostimportant sources for the LISA detector, face several computational challenges. We present a new approach to evolving partial differential equations occurring in black hole perturbation ...
Barack, Leor +3 more
core +1 more source
Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations [PDF]
, 2013 We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time.
Bandle C. +6 more
core +1 more source
Stability of Chebyshev collocation methods
Computers & Mathematics with Applications, 2004 AbstractIn [1], a class of global collocation methods for the numerical solution of systems of nonlinear first-order ordinary differential equations was derived.The favorable comparison with other existing methods stimulated us to study them in depth.
COSTABILE F, NAPOLI, Anna
openaire +3 more sources