On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae

DOI10.1137/0725049zbMath0658.65070OpenAlexW2091795718MaRDI QIDQ3806709

Jeff R. Cash

Publication date: 1988

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0725049

zbMATH Keywords

stabilityhigh-order methodsstiff problemsvariable-orderlinear test problemsimplicit deferred correctionsIterated deferred correction methodstype-insensitive method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (23)

Algebraic conditions for high-order convergent deferred correction schemes based on Runge-Kutta-Nyström methods for second order boundary value problems ⋮ Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression ⋮ Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions ⋮ Implementation issues in solving nonlinear equations for two-point boundary value problems ⋮ A new mesh selection strategy for ODEs ⋮ Lobatto deferred correction for stiff two-point boundary value problems ⋮ A two-stage LGSM for three-point BVPs of second-order ODEs ⋮ On the numerical solution of a class of singular two-point boundary value problems ⋮ Defect Correction for Two-Point Boundary Value Problems on Nonequidistant Meshes ⋮ High-order convergent deferred correlation schemes based on parameterized Runge-Kutta-Nyström methods for second-order boundary value problems ⋮ Solving second-order singularly perturbed ODE by the collocation method based on energetic Robin boundary functions. ⋮ Runge-Kutta methods for the solution of stiff two-point boundary value problems ⋮ Almost block diagonal linear systems: sequential and parallel solution techniques, and applications ⋮ A highly stable deferred correction scheme with interpolant for systems of nonlinear two-point boundary value problems ⋮ A new algorithm for calculating Adomian polynomials for nonlinear operators ⋮ OPTIMAL FLUCTUATIONS AND THE CONTROL OF CHAOS ⋮ On the method of modified equations. II: Numerical techniques based on the equivalent equation for the Euler forward difference method ⋮ A new mesh selection algorithm, based on conditioning, for two-point boundary value codes ⋮ Continuous extensions of deferred correction schemes for the numerical solution of nonlinear two-point boundary value problems ⋮ A survey of numerical techniques for solving singularly perturbed ordinary differential equations ⋮ Nonlinear bending of the shallow spherical shells with variable thickness under axisymmetrical loads ⋮ Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids ⋮ Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems

This page was built for publication: On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae