Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations
@inproceedings{Radhakrishnan1993DescriptionAU, title={Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations}, author={Krishnan Radhakrishnan and Alan C. Hindmarsh}, year={1993} }
LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user…
Tables from this paper
552 Citations
FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs
- Computer ScienceSIAM J. Sci. Comput.
- 2014
The paper describes the capabilities, implementation, code organization, and usage of the Fatode package, the first publicly available general purpose package that offers forward and adjoint sensitivity analysis capabi...
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
- Computer ScienceTOMS
- 2005
The current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness, are described.
An Efficient Implementation of the Method of Lines for Multicomponent Reactive Transport Equations
- Mathematics
- 2011
Numerical experiments show that higher-order time integration is effective for solving the non-conservative formulation and point out the high benefit of the MOL for solving reactive transport problems.
Boundary Value Methods for the Numerical Approximation of Ordinary Differential Equations
- Computer Science, MathematicsWNAA
- 1996
Many numerical methods for the approximation of ordinary differential equations (ODEs) are obtained by using Linear Multistep Formulae (LMF). Such methods, however, in their usual implementation…
Comparison of 4 numerical solvers for stiff and hybrid systems simulation
- Computer Science2010 IEEE 15th Conference on Emerging Technologies & Factory Automation (ETFA 2010)
- 2010
Four popular solvers are assessed, including DASSL, LSODAR, DOPRI5, RADAU IIA, included in the all-purpose simulator Dymola® for different problems with continuous, stiff, and hybrid behavior.
Using Diagonally Implicit Multistage Integration Methods for Solving Ordinary Differential Equations. Part 2: Implicit Methods.
- Computer Science
- 1997
Results of successful tests on the Prothero-Robinson problem are reported and demonstrate that DIMSIMs may be used to develop efficient stiff solvers, and some new A-stable and L-stable methods are derived.
Test of numerical methods for the integration of kinetic equations in tropospheric chemistry
- Computer Science
- 1999
odeToJava: A PSE for the Numerical Solution of IVPs
- Computer ScienceACM Trans. Math. Softw.
- 2015
Problem-solving environments (PSEs) offer a powerful yet flexible and convenient means for general experimentation with computational methods, algorithm prototyping, and visualization and…
Blended General Linear Methods based on Boundary Value Methods in the GBDF family
- Computer Science, Mathematics
- 2010
A new family of L-stable GLMs of arbitrarily high order is proposed, resulting in a new class of General Linear Methods with the definition of efficient nonlinear splittings for solving the generated discrete problems.
Fourth-Order Runge–Kutta Schemes for Fluid Mechanics Applications
- Computer ScienceJ. Sci. Comput.
- 2005
Multiple high-order time-integration schemes are used to solve stiff test problems related to the Navier–Stokes (NS) equations. The primary objective is to determine whether high-order schemes can…
References
SHOWING 1-9 OF 9 REFERENCES
LSODE and LSODI, two new initial value ordinary differential equation solvers
- Computer ScienceSGNM
- 1980
Two new packages are available for the numerical solution of the initial value problem for stiff and nonstiff systems of ordinary differential equations (ODE's). LSODE solves explicitly given ODE…
A User’s View of Solving Stiff Ordinary Differential Equations
- Computer Science
- 1979
This paper aims to assist the person who needs to solve stiff ordinary differential equations by identifying the problem area and the basic difficulty and describing the characteristics shared by methods for the numerical solution of stiff problems.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
- Computer Science
- 1984
An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.
ODEPACK: A Systematized Collection of ODE Solvers
- Scientific Computing,
- 1983
New integration techniques for chemical kinetic rate equations. II - Accuracy comparison
- Computer Science
- 1986
An important finding is that an iterative solution of the algebraic enthalpy conservation equation for the temperature can be more accurate and efficient than computing the temperature by integrating its time derivative.
What is Stiffness? Stiff Computation, R.C
- 1985