Solving initial value problems for ordinary differential equations by two approaches: BDF and piecewise-linearized methods

DOI10.1016/j.cpc.2008.11.013zbMath1198.65142OpenAlexW2020323687MaRDI QIDQ603316

Pedro A. Ruiz, Jacinto-Javier Ibáñez, Enrique Arias, Vicente G. Hernández

Publication date: 6 November 2010

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10251/51582

zbMATH Keywords

ordinary differential equation (ODE)piecewise-linearized method\texttt{BLAS}\texttt{LAPACK}backward differentiation formula (BDF) methoddiagonal Padé approximationinitial value problem (IVP)

Mathematics Subject Classification ID

Numerical methods for ordinary differential equations (65L99) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

Related Items (4)

A piecewise-linearized algorithm based on the Krylov subspace for solving stiff ODEs ⋮ A numerical algorithm for solving stiff ordinary differential equations ⋮ Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants ⋮ New Scaling-Squaring Taylor Algorithms for Computing the Matrix Exponential

Uses Software

• LAPACK
• Matlab
• ScaLAPACK
• VODE
• BLAS
• RODAS
• DIFSUB
• KELLEY
• bvp4c
• MPI
• MATLAB expm

Cites Work

• Piecewise-linearized methods for initial-value problems
• Piecewise-linearized and linearized \(\vartheta\)-methods for ordinary and partial differential equations.
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• An extended set of FORTRAN basic linear algebra subprograms
• VODE: A Variable-Coefficient ODE Solver
• ScaLAPACK Users' Guide
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Solving ODEs with MATLAB
• Integration of Stiff Equations
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