JVODE

Java Variable-Coefficient ODE (JVODE) solver is a ported to java version of CVODE - part of a software family SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic equation Solvers developed by Lawrence Livermore National Library. JVODE solves ordinary differential equations initial value problems with either stiff and non-stiff systems. It was refactored from CVODE into one ODE solver and user can specify which integration method will be used.

User-provided solver parameters:

• Absolute tolerance. Absolute error, is used to adjust time step during simulation.
• Relative tolerance. Relative error, is used to adjust time step during simulation.
• Statistics mode. Indicates how much information will be presented to user during simulation.
• Integration method. Two linear multistep implicit methods are available:
  • Adams - Moulton (recommended for non-stiff systems),
  • Backward Differential Formula (recommended for stiff systems).
• Inner linear solver type. Method for solving non-linear equation on each time step. Available methods are:
  • Functional iterations.
  • Newton iterations (Using linear equation system solving and Jacobian approximation).
• Jacobian approximation type. In Newton iterations case user should also define type for Jacobian approximation (user-provided Jacobian is not supported yet):
  • Dense, (recommended)
  • Banded,
  • Diagonal.
• Steps limit - maximum number of integration steps.
• Minimum time step - minimal size of time step.
• Maximum time step inverted - inversed maximal size of time step.
• Mu, Ml. Additional parameters for banded Jacobian approximation only. Note Mu and Ml must be such that: 0 < Mu, Ml < N, where N is system dimension.

References

1. P.N.Brown, G.D. Byrne, and A.C. Hundmarsh, VODE, a Variable-Coefficient ODE Solver, SIAM J. Sci. Stat. Comput., 10 (1989), pp. 1038-1051
2. S. D. Cohen, A.C. Hindmarsh, CVODE, A Stiff/Nonstiff ODE Solver in C.