Class I1a2: Stiff and mixed algebraic-ordinary differential equations
Modules
Package CMLIB (Downloadable; Installed on ITL, ARNO)
- CDRIV1
- Numerical integration of complex initial value problems for ordinary differential equations, Gear stiff formulas. Easy to use.
- CDRIV2
- Numerical integration of complex initial value problems for ordinary differential equations, Gear stiff and Adams formulas, root finding.
- CDRIV3
- Numerical integration of complex initial value problems for ODEs, Gear and Adams formulas, implicit equations, sparse Jacobians, root finding.
- DDASSL
- Solves the system of differential/algebraic equations of the form g(t,y,yprime)=0, with given initial values.
- DDRIV1
- Numerical integration, initial value problems, ordinary differential equations, Gear stiff formulas. Easy to use.
- DDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
- DDRIV3
- Numerical integration, initial value problems, ordinary differential equations, implicit equations, sparse Jacobians.
- DEBDF
- Solves a system of first order stiff ordinary differential equations with arbitrary initial conditions by Gear''s method.
- SDASSL
- Solves the system of differential/algebraic equations of the form g(t,y,yprime)=0, with given initial values.
- SDRIV1
- Numerical integration, initial value problems, ordinary differential equations, Gear stiff formulas. Easy to use.
- SDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
- SDRIV3
- Numerical integration, initial value problems, ordinary differential equations, implicit equations, sparse Jacobians.
Package IMSLM (Installed on ITL)
- DASPG
- Solve a first order differential-algebraic system of equations, g(t,y,y'')=0, using the Petzold--Gear BDF method.
- DDASPG
- Solve a first order differential-algebraic system of equations, g(t,y,y'')=0, using the Petzold--Gear BDF method.
Package MANPAK (Downloadable)
- DAEPAK
- Solves algebraically explicit differential algebraic equations (DAEs); that is, DAEs in which either the algebraic equations and/or variables are explicitly specified. Includes DAEN1 (nonlinear, index 1 problems), DAEN2 (nonlinear, index-2 problems), DAEQ2 (quasi-linear, index-2 problems), DAEQ3 (quasi-linear, index-3 problems of second order), DAESQ1 (quasi-linear, autonomous, index-1 problems) DAEUL3 (EUler Lagrange problem of index 3).
Package NAG
- D02EJF
- Ordinary differential equations, stiff initial value problem, backward diffential formulae method, until function of solution is zero, intermediate output (simple driver)
- D02NBF
- Explicit ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
- D02NCF
- Explicit ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
- D02NDF
- Explicit ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
- D02NGF
- Implicit/algebraic ordinary differential equations, stiff initial value problem, full Jacobian (comprehensive)
- D02NHF
- Implicit/algebraic ordinary differential equations, stiff initial value problem, banded Jacobian (comprehensive)
- D02NJF
- Implicit/algebraic ordinary differential equations, stiff initial value problem, sparse Jacobian (comprehensive)
- D02NMF
- Explicit ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
- D02NNF
- Implicit/algebraic ordinary differential equations, stiff initial value problem (reverse communication, comprehensive)
- D03PKF
- General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
- D03PPF
- General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
- D03PRF
- General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
- d02ejc
- Ordinary differential equations solver, stiff, initial value problems using the Backward Differentiation Formulae
- d03pkc
- General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, one space variable
- d03ppc
- General system of parabolic PDEs, coupled DAEs, method of lines, finite differences, remeshing, one space variable
- d03prc
- General system of first-order PDEs, coupled DAEs, method of lines, Keller box discretisation, remeshing, one space variable
Package NMS (Installed on ITL)
- DDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
- SDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
Package ODE (Downloadable)
- CVODE
- Solves the initial value problem for stiff or nonstiff nonlinear systems of first order ordinary differential equations using variable-coefficient forms of the Adams and backward differentiation formulae (linear multistep methods). Appropriate for systems with dense, banded, or sparse Jacobians. In the latter case a preconditioned Krylov interative method (GMRES) is used. (By: Scott D. Cohen and Alan C. Hindmarsh, 1994).
- DDASRT
- Solves a system of differential/algebraic equations of the form F(T,Y,YPRIME) = 0 using the backward differentiation formulas of orders one through five. Includes an intermediate-output capability. If SDASRT detects a sign-change in the user-defined function G(T,Y), then it will return the intermediate value of T and Y for which G(T,Y) = 0. (By: L. Petzold, 1991).
- DDASSL
- Solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0 using backward differentiation formulas of orders one through five. (By: L. Petzold, 1991).
- DGELDA
- Solves GEneral Linear Differential-Algebraic equations with variable coefficients. Handles systems of arbitrary index and with those with non-unique solutions or inconsistencies in the initial values or the inhomogeneity. Includes a computation of all local invariants of the system, a regularization procedure and an index reduction scheme. Developed by P. Kunkel, V. Mehrmann, W. Rath and J. Weickert.
- DRESOL
- Numerical integration of matrix Riccati differential equations, i.e. dX/dt = A21(t) + A22(t)*X - X*A11(t) - X*A12(t)*X, plus appropriate initial conditions. Both symmetric and nonsymmetric systems are handled. Based on the LSODE software of Hindmarsh. Developed by Luca Dieci (dieci@math.gatech.edu).
- EPSODE
- A stiff ordinary differential equation initial-value problem solver based on variable coefficient backward differentiation formula. (By: A.C. Hindmarsh and G.D. Byrne, 1975).
- MEBDFDAE
- Solves stiff initial value problems and differential algebraic equations in linearly implicit form. Based on modified extended backward differentiation formulae which have better stability than BDF and are A-Stable up to order 4 and A(alpha)-Stable up to order 9. More recent version of MEBDF routine published as TOMS algorithm 703. (By J.R. Cash, 1997).
- PARSODES
- A parallel stiff ODE initial-value problem solver based on an across the method parallelization of multi-implicit Runge-Kutta (MIRK) methods. Based on MPI message passing. Shows good performance and parallel speedup for large systems. Developed by Claus Bendtsen (Claus.Bendtsen@uni-c.dk).
- SDASRT
- Solves a system of differential/algebraic equations of the form F(T,Y,YPRIME) = 0 using the backward differentiation formulas of orders one through five. Includes an intermediate-output capability. If SDASRT detects a sign-change in the user-defined function G(T,Y), then it will return the intermediate value of T and Y for which G(T,Y) = 0. (By: L. Petzold, 1991).
- SDASSL
- Solves a system of differential/algebraic equations of the form G(T,Y,YPRIME) = 0 using backward differentiation formulas of orders one through five. (By: L. Petzold, 1991).
- SVODE
- Solves the initial value problem for stiff or nonstiff systems of first order ordinary differential equations using variable-coefficient backward differentiation formulae with fixed-leading coefficient. Updated version of EPSODE. (By: P.N. Brown, G.D. Byrne, and A.C. Hindmarsh, 1991).
- SVODPK
- Solves the initial value problem for stiff or nonstiff systems of first order ordinary differential equations using variable-coefficient backward differentiation formulae with fixed-leading coefficient. Uses preconditioned Krylov method GMRES for the solution of linear systems. Appropriate for solution of large systems on vector computers. (By: P.N. Brown, G.D. Byrne, and A.C. Hindmarsh, 1991).
- VODE
- Solves the initial value problem for stiff or nonstiff systems of first order ordinary differential equations using variable-coefficient backward differentiation formulae with fixed-leading coefficient. Updated version of EPSODE. (By: P.N. Brown, G.D. Byrne, and A.C. Hindmarsh, 1991).
- VODPK
- Solves the initial value problem for stiff or nonstiff systems of first order ordinary differential equations using variable-coefficient backward differentiation formulae with fixed-leading coefficient. Uses preconditioned Krylov method GMRES for the solution of linear systems. Appropriate for solution of large systems on vector computers. (By: P.N. Brown, G.D. Byrne, and A.C. Hindmarsh, 1991).
Package ODEPACK (Downloadable)
- DLSODA
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Automatically selects between Adams (nonstiff) and Backward Differentiation Formula (stiff) methods. In the stiff case, the Jacobian matrix may be full or banded, and either user-supplied or internally approximated by difference quotients. Resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and L.R. Petzold).
- DLSODAR
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Automatically selects between Adams (nonstiff) and Backward Differentiation Formula (stiff) methods. In the stiff case, the Jacobian may be full or banded, and either user-supplied or internally approximated. Resulting linear systems solved by direct methods. Has rootfinding capability. (By: A.C. Hindmarsh and L.R. Petzold).
- DLSODE
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. In the stiff case, the Jacobian matrix may be full or banded, and either user-supplied or internally approximated by difference quotients. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh).
- DLSODES
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. In the stiff case, it treats the Jacobian matrix in general sparse form, with the sparsity structure determined on its own or by the user. The Yale Sparse Matrix Package is used to solve the linear systems that arise. (By: A.C. Hindmarsh and A.H. Sherman).
- DLSODI
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices may be full or banded, and the Jacobian may be either user-supplied or internally approximated by difference quotients. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and J.F. Painter).
- DLSODIS
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices are assumed to be sparse, with the sparsity structure determined on its own or by the user. Uses parts of the Yale Sparse Matrix Package to solve the linear systems that arise, by a direct method. (By: A.C. Hindmarsh and S. Balsdon).
- DLSODKR
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Selects between Adams and BDF methods. Resulting linear systems solved by a selection of four preconditioned Krylov (iterative) solvers. User must supply a pair of routine to evaluate, preprocess, and solve the preconditioner matrices. Option for user-supplied linear system solver to use without Krylov iteration and rootfinding capability. (By: Hindmarsh and Brown).
- DLSODPK
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Selects between Adams and BDF methods. Resulting linear systems solved by a selection of four preconditioned Krylov (iterative) solvers. User must supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Option for a user-supplied linear system solver to use without Krylov iteration. (By: A.C. Hindmarsh and P. N. Brown).
- DLSOIBT
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices are assumed to be block-tridiagonal, and the Jacobian may be either user-supplied or internally approximated. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and C.S. Kenney).
Package SLATEC (Downloadable; Installed on ITL, ARNO)
- CDRIV1
- Numerical integration of complex initial value problems for ordinary differential equations, Gear stiff formulas. Easy to use.
- CDRIV2
- Numerical integration of complex initial value problems for ordinary differential equations, Gear stiff and Adams formulas, root finding.
- CDRIV3
- Numerical integration of complex initial value problems for ODEs, Gear and Adams formulas, implicit equations, sparse Jacobians, root finding.
- DDASSL
- Solves the system of differential/algebraic equations of the form g(t,y,yprime)=0, with given initial values.
- DDEBDF
- Solve an initial value problem in ordinary differential equations using backward differentiation formulas. It is intended primarily for stiff problems.
- DDRIV1
- Numerical integration, initial value problems, ordinary differential equations, Gear stiff formulas. Easy to use.
- DDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
- DDRIV3
- Numerical integration, initial value problems, ordinary differential equations, implicit equations, sparse Jacobians.
- DEBDF
- Solve an initial value problem in ordinary differential equations using backward differentiation formulas. It is intended primarily for stiff problems.
- SDASSL
- Solves the system of differential/algebraic equations of the form g(t,y,yprime)=0, with given initial values.
- SDRIV1
- Numerical integration, initial value problems, ordinary differential equations, Gear stiff formulas. Easy to use.
- SDRIV2
- Numerical integration, initial value problems, ordinary differential equations, Gear/Adams formulas.
- SDRIV3
- Numerical integration, initial value problems, ordinary differential equations, implicit equations, sparse Jacobians.
Package SODEPACK (Downloadable)
- SLSODA
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Automatically selects between Adams (nonstiff) and Backward Differentiation Formula (stiff) methods. In the stiff case, the Jacobian matrix may be full or banded, and either user-supplied or internally approximated by difference quotients. Resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and L.R. Petzold).
- SLSODAR
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Automatically selects between Adams (nonstiff) and Backward Differentiation Formula (stiff) methods. In the stiff case, the Jacobian may be full or banded, and either user-supplied or internally approximated. Resulting linear systems solved by direct methods. Has rootfinding capability. (By: A.C. Hindmarsh and L.R. Petzold).
- SLSODE
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. In the stiff case, the Jacobian matrix may be full or banded, and either user-supplied or internally approximated by difference quotients. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh).
- SLSODES
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. In the stiff case, it treats the Jacobian matrix in general sparse form, with the sparsity structure determined on its own or by the user. The Yale Sparse Matrix Package is used to solve the linear systems that arise. (By: A.C. Hindmarsh and A.H. Sherman).
- SLSODI
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices may be full or banded, and the Jacobian may be either user-supplied or internally approximated by difference quotients. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and J.F. Painter).
- SLSODIS
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices are assumed to be sparse, with the sparsity structure determined on its own or by the user. Uses parts of the Yale Sparse Matrix Package to solve the linear systems that arise, by a direct method. (By: A.C. Hindmarsh and S. Balsdon).
- SLSODKR
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Selects between Adams and BDF methods. Resulting linear systems solved by a selection of four preconditioned Krylov (iterative) solvers. User must supply a pair of routine to evaluate, preprocess, and solve the preconditioner matrices. Option for a user-supplied linear system solver to use without Krylov iteration and rootfinding capability. (By: Hindmarsh and Brown).
- SLSODPK
- Solves initial-value problems for stiff and nonstiff systems of ordinary differential equations. Selects between Adams and BDF methods. Resulting linear systems solved by a selection of four preconditioned Krylov (iterative) solvers. User must supply a pair of routine to evaluate, preprocess, and solve the (left and/or right) preconditioner matrices. Option for a user-supplied linear system solver to use without Krylov iteration.(By: A.C. Hindmarsh and Peter N. Brown).
- SLSOIBT
- Solves linearly-implicit initial-value problems for stiff and nonstiff systems of ordinary differential equations. Both Adams (nonstiff), and Backward Differentiation Formula (stiff) methods are used. All matrices are assumed to be block-tridiagonal, and the Jacobian may be either user-supplied or internally approximated. The resulting linear systems solved by direct methods (LU factor/solve). (By: A.C. Hindmarsh and C.S. Kenney).
Package TOMS (Downloadable)
- 534
- STINT: A Fortran subprogram for integrating a set of first order ordinary differential equations using stiffly stable, cyclic composite linear multistep methods. (See J.M. Tendler, T.A. Bickart, and Z. Picel, ACM TOMS 4 (1978) pp. 399-403.).
- 658
- ODESSA: A Fortran ordinary differential equation solver (a modification of LSODE) with explicit simultaneous sensitivity analysis. (See J. R. Leis and M. A. Kramer, ACM TOMS 14 (1988) pp. 61-67.).
- 703
- MEBDF: Solves first-order systems of stiff initial value problems for ordinary differential equations using a class of modified extended backward differentiation formulas. (See J. Cash and S. Considine, ACM TOMS 18 (1992) pp. 142-158.).