The BiM code for the numerical solution of ODEs.

DOI10.1016/j.cam.2003.09.004zbMath1038.65063OpenAlexW2149255560MaRDI QIDQ1426764

Cecilia Magherini, Luigi Brugnano

Publication date: 15 March 2004

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.2003.09.004

zbMATH Keywords

Numerical examplesStiff problemsNumerical softwareInitial value problemsBlended implicit methodsCode BiMComparison methodsNonlinear splittings

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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)

Related Items (21)

Blended implicit methods for the numerical solution of DAE problems ⋮ Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations ⋮ Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems ⋮ Spectrally accurate space-time solution of Manakov systems ⋮ Blended implicit methods for solving ODE and DAE problems, and their extension for second-order problems ⋮ On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems ⋮ Arbitrarily high-order energy-conserving methods for Poisson problems ⋮ Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles ⋮ Energy-conserving methods for the nonlinear Schrödinger equation ⋮ Line integral solution of Hamiltonian systems with holonomic constraints ⋮ A test set for stiff initial value problem solvers in the open source software R: Package \textbf{deTestSet} ⋮ A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator ⋮ A note on the efficient implementation of Hamiltonian BVMs ⋮ Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation ⋮ Efficient implementation of Radau collocation methods ⋮ Efficient implementation of Gauss collocation and Hamiltonian boundary value methods ⋮ Energy conservation issues in the numerical solution of the semilinear wave equation ⋮ Economical error estimates for block implicit methods for ODEs via deferred correction. ⋮ Recent advances in linear analysis of convergence for splittings for solving ODE problems ⋮ Line integral solution of differential problems ⋮ BiM

Uses Software

• MEBDF
• RODAS
• BiMD

Cites Work

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• Solving ordinary differential equations by generalized Adams methods: Properties and implementation techniques
• Parallel linear system solvers for Runge-Kutta methods
• Blended implementation of block implicit methods for ODEs
• Blended block BVMs (B\(_3\)VMs): A family of economical implicit methods for ODEs
• Economical error estimates for block implicit methods for ODEs via deferred correction.
• Triangularly Implicit Iteration Methods for ODE-IVP Solvers
• Some linear algebra issues concerning the implementation of blended implicit methods
• An MEBDF code for stiff initial value problems
• A-stable block implicit one-step methods

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