A first course in the numerical analysis of differential equations

By A. Iserles. 1996

Citations in the corpus

Mean value coordinates (2003, unknown): “These weights arise from the standard piecewise linear finite element approximation to the Laplace equation and appear in several books on numerical analysis, e.g., ( Iserles, 1996 ), and probably go back to the work of Courant.”
A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, unknown): “Because L is eﬀectively a ﬁnite-diﬀerence discretization of Poisson’s equation on a regular grid with homogeneous Dirichlet boundary conditions, application of L ´ 1 may be accomplished with the FFT at a cost of O p N log N q using typical fast Poisson solver techniques [28, Chapter 12].”
ON THE ACCURACY OF FINITE DIFFERENCE METHODS FOR ELLIPTIC PROBLEMS WITH INTERFACES (2006, unknown): “In dimension d D 2, the nine-point Laplacian (see, for example, [19], Section 7.”
Bespoke Solvers for Generative Flow Models (2023, unknown): “A popular family of solvers that offers a wide range of orders is the Runge-Kutta (RK) family (Iserles, 2009).”
Geometric integrators for ODEs (2006, unknown): “The class of method, its order and local error, and choice of time steps are all tailored to this end [20, 21, 49, 57 ].”
On the Global Error of Discretization Methods for Highly-Oscillatory Ordinary Differential Equations (2002, unknown): “and solve it with a p-order Runge–Kutta method [10, 14 ].”
MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster (2012, unknown): “…J which may be solved, using a banded matrix solver, in O J 4 (cid:0) (cid:1) As drawing a sample is a O (cid:0) J 4 (cid:1) operation, the grid sizes used within these experiments was kept deliberately low: for target deﬁned via κ we take J = 64. ﬂoating point operations (see p. 171 [32]).”