2.7.4 NDAESolve Options

Options[NDAESolve]

Several options are available for NDAESolve most of which need not be changed unless there are problems with the default settings, such as convergence problems. To list all options associated with NDAESolve inspect the value of Options[NDAESolve]:

In[21]:= Options[NDAESolve]

Out[23]=

Below, a set of NDAESolve options is explained in more detail:

InitialGuess

With the default setting InitialGuess -> Automatic, zero is used as initial guess for all variables when solving a system of nonlinear equations by means of Newton iterations. Whenever this setting causes numerical problems, such as division-by-zero errors or failure to converge, you can use InitialGuess to specify your own initial guess as a list of rules of the form:

InitialGuess -> -> , , ->

Note that the variables are specified without the time variable .

InitialSolution

With the option InitialSolution we can force NDAESolve to use a certain DC solution as initial operating point for a transient analysis. A set of initial values must be provided as a list of rules which associate a numerical value with a variable from the system of equations. Missing variables are then computed consistently.

InitialSolution -> -> , , ->

Note that the variables are specified without the time variable .

MaxDelta

One of the conditions that are checked by the integration step size control mechanism is whether the values of some variables change abruptly from one time step to the next. The maximum allowed difference between two successive values is controlled by the option MaxDelta. The default setting is MaxDelta -> 1.0. This value is large enough to allow sudden steps of input voltages which are quite usual in the case of pulse excitations.

MaxIterations

The option MaxIterations specifies the maximum number of steps that the nonlinear equation solver should use in attempting to find a solution. The option setting can either be an integer or a list of two integers . If it is specified as a single integer then it is equivalent to the list . The first integer value defines the iteration limit for finding a DC operating point and the second integer value the iteration limit for transient computations, respectively. If the number of iterations for the operating-point computation exceeds the limit, an error message is generated and the computation is interrupted. If the iteration limit for transient computations is exceeded, the step size is reduced by the factor given by the option StepSizeFactor. The default setting is MaxIterations -> {100, 20}.

MaxSteps

The option MaxSteps limits the total number of integration steps. The simulation is stopped immediately if the limit is exceeded. The default setting is MaxSteps -> Automatic, which means .

MaxStepSize

It is sometimes possible to speed up simulations by allowing a larger maximum integration step size. With the option MaxStepSize the present step size limit can be extended or reduced. The default setting is MaxStepSize -> Automatic, which means .

MinStepSize

The lower limit of the integration step size can be specified by the option MinStepSize. NDAESolve stops a simulation immediately if the integration step size falls below this limit. The default setting is MinStepSize -> Automatic, which means .

NonlinearMethod

The option NonlinearMethod chooses among different numerical algorithms for solving the nonlinear algebraic systems of equations which arise due to the discretization of DAEs. By default, Mathematica's numerical solver FindRoot is used for this purpose. Alternatively, you can employ Analog Insydes' own implementation of the multi-dimensional Newton-Raphson method by specifying NonlinearMethod -> NewtonIteration.

Protocol

With the option setting Protocol -> Notebook, NDAESolve can be instructed to print protocol information to your notebook as the computation proceeds. The protocol includes an output of the initial guess, the initial transient solution, shows the percentage of the computation completed, and the number of time steps which were necessary to carry out the computation. The default setting is Protocol -> Inherited[AnalogInsydes] which means that NDAESolve inherits the option setting from the global setting specified in Options[AnalogInsydes]. See also Section 3.14.5.

StartingStepSize

The option StartingStepSize helps to overcome convergence problems at the beginning of a simulation. If NDAESolve fails to converge during the first time step you can use StartingStepSize to specify a smaller value for the initial integration step size. The default setting is StartingStepSize -> Automatic, which means .

StepSizeFactor

To reduce computation time and increase simulation accuracy NDAESolve employs an automatic step size control scheme. If the estimated simulation error in between two integration time steps is very low then the step size is increased. On the other hand, if the estimated error is too large the step size is cut back. Increasing and reducing the step size is performed by multiplying or dividing the current step size by a factor given by the value of the option StepSizeFactor. The default setting is StepSizeFactor -> 1.5.