DDAE: an integrator for ODEs, DAEs and DDEs, part I

Abstract

DDAE is a variable order, variable stepsize Adams and BDF Fortran integrator for solving initial-value ordinary differential equations (ODEs), initial-value differential-algebraic equations (DAEs) of index 0 and 1, and delay differential equations (DDEs). The differential equations can be mixed order, and the DDEs can have both state-dependent and multiple delays and can include DAEs. DDAE has a large number of optional inputs. Options permit the user to perform a wide range of tasks and to take advantage of features of a problem to improve efficiency. The options include those for varying the interpolation, saving the solution, controlling the stepsize and order selection, and solving for g-stops. DDAE also has reverse communication (returning to the driver calling DDAE for function evaluations) as an option. This makes it easy for the user to call DDAE from other software and to use special software for solving linear equations. A distinctive feature of DDAE is the ability to group the equations and use different options for different groups. This can lead to a marked reduction in the CPU time. For example, the equations could be divided into non-stiff and stiff equations, and Adams and BDF methods used for the two groups respectively. This report summarises the features of DDAE with an emphasis on the options.