Journal of Computational Physics
Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels
Mathematics of Computation
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Journal of Computational Physics
Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems
Journal of Computational Physics
Journal of Scientific Computing
Fredholm integral equation method for the integro-differential Schrödinger equation
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
An extension of trapezoidal type product integration rules
Journal of Computational and Applied Mathematics
Stable high-order quadrature rules with equidistant points
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
Fast integral equation methods for Rothe's method applied to the isotropic heat equation
Computers & Mathematics with Applications
Quadrature rules for numerical integration based on Haar wavelets and hybrid functions
Computers & Mathematics with Applications
Journal of Computational Physics
Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator
Journal of Computational Physics
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
SIAM Journal on Scientific Computing
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
Journal of Computational Physics
Advances in Computational Mathematics
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A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily high-order convergence. The quadratures result from alterations to the trapezoidal rule, in which a small number of nodes and weights at the ends of the integration interval are replaced. The new nodes and weights are determined so that the asymptotic expansion of the resulting rule, provided by a generalization of the Euler--Maclaurin summation formula, has a prescribed number of vanishing terms. The superior performance of the rules is demonstrated with numerical examples and application to several problems is discussed.