D02mn (Ode)

Ordinary Differential EquationsIntegrators for Stiff Ordinary Differential Systems

This sub-chapter contains the specifications of the integrators
from the
DASSL package, Brenan et al. (1996).

The DASSL integrator d02nec is designed for solving systems of the form, $F\left(t,y,y\prime \right)=0$. These formulations permit solution of differential/algebraic systems
(DAEs). The facilities provided are essentially those of the explicit solvers.

The DASSL integrator, d02nec, has an associated setup function d02mwc which must be called first. On return from the integrator, if it is feasible to continue the integration, the associated continuation call function is d02mcc may be called to rest various integration parameters. The structure of the Jacobian is assumed to be full unless d02npc is called following a call to the setup function to specify that the Jacobian is banded and to supply its bandwidths.

The DASSL integrator d02nec can solve DAEs of the fully implicit form $F\left(t,y,y\prime \right)=0$ and therefore has increased functionality over the SPRINT integrators. Additionally
d02nec can be used to solve difficult algebraic problems by continuation; for example, the nonlinear algebraic problem

can be solved by integrating solutions of

where the solution to $f\left(x\right)+g\left(x\right)=0$ is known. The solution of this type of problem is illustrated in Section 10 in **d02nec**.

$$f\left(x\right)=0$$ |

$$f\left(x\right)+\left(1-t\right)g\left(x\right)=0$$ |

Berzins M and Furzeland R M (1985) A user's manual for SPRINT – A versatile software package for solving systems of algebraic, ordinary and partial differential equations: Part 1 – Algebraic and ordinary differential equations *Report TNER.85.085* Shell Research Limited

Brenan K, Campbell S and Petzold L (1996) *Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations* SIAM, Philadelphia