Variable Order Adams-Bashforth Predictors with an Error-Stepsize Control for Continuation Methods

DOI10.1137/0912037zbMath0737.65042OpenAlexW2036949505MaRDI QIDQ4713427

Bruce N. Lundberg, Aubrey B. Poore

Publication date: 25 June 1992

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0912037

zbMATH Keywords

numerical examplespath-following methodlocal extrapolationDavidenko equationarclength parametrizationefficient and robust algorithmconsecutive order methodserror- stepsize controlNewton-like correctionpredictor-corrector continuation methodsvariable order Adams-Bashford predictors

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

Design and evaluation of homotopies for efficient and robust continuation ⋮ Efficient numerical differentiation of implicitly-defined curves for sparse systems ⋮ Cubic spline interpolation predictors over implicitly defined curves ⋮ Interpolation predictors over implicitly defined curves. ⋮ Robust continuation methods for tracing solution curves of parameterized systems ⋮ High-order polynomial continuation method for trajectory design in non-Keplerian environments ⋮ Bifurcations in parametric nonlinear programming ⋮ Advances in trust region algorithms for constrained optimization

Uses Software

• PITCON
• ALCON
• HOMPACK

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