On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs

DOI10.1007/s11075-015-0027-1zbMath1338.65191OpenAlexW1643578649MaRDI QIDQ281474

Truong Nguyen-Ba

Publication date: 11 May 2016

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-015-0027-1

zbMATH Keywords

algorithmstabilitynumerical examplecomparison of methodsRunge-Kutta methodbackward differentiation formulaestepsize controlconfluent Vandermonde-type systemsendpoint errorHermite-Birkhoff methodlocal error estimatormethod for stiff ODEsmultistepnumber of stepsstiff DETEST problems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical methods for stiff equations (65L04)

Related Items (1)

Generalized linear multistep methods for ordinary differential equations

Uses Software

• MEBDF
• DASSL
• RODAS
• A-EBDF
• NSDTST
• STDTST

Cites Work

• Perturbed MEBDF methods
• Three-stage Hermite-Birkhoff solver of order 8 and 9 with variable step size for stiff ODEs
• The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae
• A-EBDF: An adaptive method for numerical solution of stiff systems of ODEs
• On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
• Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs
• New second derivative multistep methods for stiff systems
• Algorithms for confluent Vandermonde systems
• On Numerical Integration of Ordinary Differential Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Numerical comparisons of some explicit Runge-Kutta pairs of orders 4 through 8
• An MEBDF code for stiff initial value problems
• Solving Nonlinear Equations with Newton's Method
• Two FORTRAN packages for assessing initial value methods
• Solution of Vandermonde systems of equations
• Comparing Numerical Methods for Ordinary Differential Equations
• Solving confluent Vandermonde systems of Hermite type
• Hybrid BDF methods for the numerical solutions of ordinary differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On variable step Hermite-Birkhoff solvers combining multistep and 4-stage DIRK methods for stiff ODEs