I. User input (by a friendly interface) :

• Define the problem variables.
• Define the right side of the ODE system (for example f from y'=f(y) ).
• Establish the integration interval.
• Establish the initial values.

II. Expert decisions:

• system linearity;
• sparsely and separable (for information storage schemes);
• problem classification in the idea to select a numerical method (for example, a stiff-nonstiff classification).

I. User input (by a friendly interface):

• Define the method variables.
• Define the equations at one step of the iterative process.
• Define the relationships between the old variables and the new variables in the reiteration case.
• Define the starting values in the case of a multistep method.
• Define a procedure as an implicit equation solver and a starting value for this procedure.
• Define a scheme for the error control.

II. Expert decisions:

• basic method classification (onestage/multistage, onestep/multistep, explicit/implicit, onederivative/multiderivative etc.);
• method order and method error;
• method stability;
• recommendation for a specific problem class.

I. User input (by a friendly interface ):

• error control;
• time control.

II. Expert decisions:

• abort computation in special cases;
• interpret the intermediate results;
• manipulate schemes with variable stepsize and variable formulae;
• reduce the computation time using concurrent computations.