The Defect Correction Approach

Lecture Notes in Mathematics

2007 • 10,414 citations

Multi-level adaptive solutions to boundary-value problems

1977 • 3,170 citations

Numerical treatment of ordinary differential equations by extrapolation methods

1966 • 827 citations

Numerical Solution of Ordinary and Partial Differential Equations

1963 • 494 citations

Analysis of Discretization Methods for Ordinary Differential Equations

1973 • 457 citations

Analysis of Discretization Methods for Ordinary Differential Equations

1974 • 429 citations

Solution of Vandermonde systems of equations

1970 • 351 citations

Black box multigrid

1982 • 328 citations

The defect correction principle and discretization methods

1978 • 278 citations

The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations.

1959 • 269 citations

Solution of Vandermonde Systems of Equations

1970 • 245 citations

On Extrapolation Algorithms for Ordinary Initial Value Problems

1965 • 240 citations

Difference Methods and Their Extrapolations

1983 • 187 citations

Difference methods and their extrapolations

1986 • 173 citations

Multigrid Solutions to Elliptic Flow Problems

1979 • 163 citations

On the estimation of errors propagated in the numerical integration of ordinary differential equations

1976 • 129 citations

Asymptotic expansions for the error of discretization algorithms for non-linear functional equations

1965 • 123 citations

Stiff Differential Systems

1974 • 118 citations

Some improvements in the use of relaxation methods for the solution of ordinary and partial differential equations

1947 • 113 citations

�ber die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode

1960 • 108 citations

Iterated deferred corrections for nonlinear operator equations

1967 • 99 citations

Iterative variants of the Nystr�m method for the numerical solution of integral equations

1974 • 94 citations

Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations

1977 • 90 citations

A Theoretical Framework for Proving Accuracy Results for Deferred Corrections

1982 • 82 citations

An adaptive, multi-level method for elliptic boundary value problems

1981 • 80 citations

The theory of orbits in the solar system and in stellar systems

1966 • 80 citations

Repeated extrapolation to the limit in the numerical solution of ordinary differential equations

1964 • 77 citations

Iterated deferred corrections for nonlinear boundary value problems

1968 • 76 citations

A method for the estimation of errors propagated in the numerical solution of a system of ordinary differential equations

1966 • 64 citations

A robust and efficient multigrid method

1982 • 62 citations

Multiple grid methods for the solution of Fredholm integral equations of the second kind

1981 • 58 citations

Accelerating the Convergence of Discretization Algorithms

1967 • 54 citations

The method of Iterated Defect-Correction and its application to two-point boundary value problems

1976 • 51 citations

Economical Global Error Estimation

1974 • 51 citations

Iterated defect correction for differential equations part I: theoretical results

1978 • 44 citations

Error estimation and iterative improvement for discretization algorithms

1980 • 42 citations

On Discretization and Differentiation of Operators with Application to Newton’s Method

1966 • 37 citations

High order fast Laplace solvers for the Dirichlet problem on general regions

1977 • 36 citations

The method of iterated defect-correction and its application to two-point boundary value problems

1975 • 32 citations

Discrete Newton methods and iterated defect corrections

1981 • 27 citations

Die schnelle Auflösung der Fredholmschen Integralgleichung zweiter Art

1981 • 27 citations

Vectorized multigrid poisson solver for the CDC cyber 205

1983 • 26 citations

Newton's method with mesh refinements for numerical solution of nonlinear two-point boundary value problems

1978 • 26 citations

Highly accurate numerical solution of casilinear elliptic boundary-value problems in 𝑛 dimensions

1970 • 24 citations

On the regularity of difference schemes Part II. Regularity estimates for linear and nonlinear problems

1983 • 19 citations

An extension of the applicability of iterated deffered corrections

1977 • 18 citations

The solution by relaxation methods of ordinary differential equations

1949 • 17 citations

Error Estimation and Iterative Improvement for the Numerical Solution of Operator Equations.

1976 • 15 citations

Asymptotic expansion for the discretization error in linear elliptic boundary value problems on general regions

1981 • 14 citations

On the order of iterated defect correction

1978 • 14 citations

Implementation of defect correction methods for stiff differential equations

1979 • 13 citations

Multigrid software for the solution of elliptic problems on rectangular domains: MGOO (release 1)

1982 • 13 citations

Error analysis of the nonlinear multigrid method of the second kind

1981 • 12 citations

A portable vector-code for autonomous multigrid modules

1984 • 7 citations

Classical Solutions of the Initial Value Problem for the Navier‐Stokes Equations with Heath Convection

1982 • 5 citations

Discrete Defect Corrections: Basic Ideas

1983 • 3 citations

Uniform expansions for a class of finite difference schemes for elliptic boundary value problems

1981 • 2 citations

Multigrid acceleration of an iterative method with application to transonic potential flow

1985 • 2 citations

Deleted Work

1955 • 0 citations