An efficient family of strongly \(A\)-stable Runge-Kutta collocation methods for stiff systems and DAEs. I: Stability and order results

DOI10.1016/j.cam.2009.05.027zbMath1191.65110OpenAlexW2078970994MaRDI QIDQ970401

S. González-Pinto, D. Hernández-Abreu, Juan I. Montijano

Publication date: 17 May 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.05.027

zbMATH Keywords

numerical examplescollocation methodsstiff systemsRunge-Kutta methodsinterpolatory quadrature formulaestrong \(A\)-stabilitydifferential algebraic equations (DAEs)

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for differential-algebraic equations (65L80)

Related Items (15)

A note on the stability of time-accurate and highly-stable explicit operators for stiff differential equations ⋮ On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line ⋮ Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements ⋮ Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed ⋮ An efficient family of strongly A-stable Runge-Kutta collocation methods for stiff systems and DAEs. II: Convergence results ⋮ Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter ⋮ Adaptive ODE solvers in extended Kalman filtering algorithms ⋮ Strongly \(A\)-stable first stage explicit collocation methods with stepsize control for stiff and differential-algebraic equations ⋮ Global error estimates for a uniparametric family of stiffly accurate Runge-Kutta collocation methods on singularly perturbed problems ⋮ NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements ⋮ Implicit Runge-Kutta methods with explicit internal stages ⋮ Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3 ⋮ A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas ⋮ Radau and Lobatto-type quadratures associated with strong Stieltjes distributions ⋮ On the global error of special Runge-Kutta methods applied to linear differential algebraic equations

Uses Software

• RODAS
• Test Set for IVP Solvers

Cites Work

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