Iterated defect correction for differential equations. I: Theoretical results

DOI10.1007/BF02251946zbMath0401.65046MaRDI QIDQ1255304

Reinhard Frank, Christoph W. Ueberhuber

Publication date: 1978

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

AccuracyBoundary Value ProblemsAsymptotic PropertiesAsymptotic AccuracyDifferential Equation ProblemsDiscretization MethodError EstimationGeneral Asymptotic Convergence ResultInitialInitial ApproximationIterated Defect CorrectionOrdinary and Partial Differential Equations

Mathematics Subject Classification ID

Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Related Items (20)

Discontinuous Galerkin schemes with defect corrections based on reconstruction ⋮ A high order time splitting method based on integral deferred correction for semi-Lagrangian Vlasov simulations ⋮ Numerical investigations on global error estimation for ordinary differential equations ⋮ Asymptotic error expansions for defect correction iterates ⋮ Local error estimates for moderately smooth problems. I: ODEs and DAEs ⋮ Implementation of defect correction methods for stiff differential equations ⋮ Pointwise error estimates of numerical solutions to linear quadratic optimal control problems ⋮ Discrete Newton methods and iterated defect corrections ⋮ The application of iterated defect correction to variational methods for elliptic boundary value problems ⋮ New finite difference methods for singularly perturbed convection-diffusion equations ⋮ Stable high order methods for differential equations with small coefficients for the second order terms ⋮ Vienna contributions to the development of RK-methods ⋮ A new way to generate an exponential finite difference scheme for 2D convection-diffusion equations ⋮ New a posteriori error estimates for singular boundary value problems ⋮ Thirteen ways to estimate global error ⋮ Diagonally implicit Runge-Kutta formulae for the numerical integration of nonlinear two-point boundary value problems ⋮ Iterated defect correction of differential equations. II: Numerical experiments ⋮ High-order finite volume schemes based on defect corrections ⋮ Modified defect correction algorithms for ODEs. II: Stiff initial value problems ⋮ Stable high order methods for elliptic equations with large first order terms

Cites Work

• On the estimation of errors propagated in the numerical integration of ordinary differential equations
• The method of iterated defect-correction and its application to two-point boundary value problems. I
• Error bounds for spline and L-spline interpolation
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
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